# MAT180-HY1 Calculus Assignment Solutions

MAT180-HY1 Calculus Assignment Solutions

The function f(x)=2×3−24×2+72x+9f(x)=2×3-24×2+72x+9 has one local minimum and one local maximum. This function has a local minimum at xx equals Incorrect with value Incorrect and a local maximum at xx equals Incorrect with value Incorrect

Question 1. Last Attempt: 0 out of 1 (parts: Incorrect 0/0.25, Incorrect 0/0.25, Incorrect 0/0.25, Incorrect 0/0.25) Score in Gradebook: 0 out of 1 (parts: Incorrect 0/0.25, Incorrect 0/0.25, Incorrect 0/0.25, Incorrect 0/0.25)

The function f(x)=2×3−39×2+240x−2f(x)=2×3-39×2+240x-2 has two critical numbers. The smaller one is x=x= Incorrect and the larger one is x=x= Incorrect .

MAT180-HY1 Calculus Assignment Solutions

Question 2. Last Attempt: 0 out of 1 (parts: Incorrect 0/0.5, Incorrect 0/0.5) Score in Gradebook: 0 out of 1 (parts: Incorrect 0/0.5, Incorrect 0/0.5)

The function f(x)=2×3−27×2+84x+11f(x)=2×3-27×2+84x+11 has derivative f'(x)=6×2−54x+84f′(x)=6×2-54x+84. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals with value and a local maximum at xx equals with value

Question 3. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=−2×3+42×2−240x+4f(x)=-2×3+42×2-240x+4 has one local minimum and one local maximum. This function has a local minimum at xx = with value and a local maximum at xx = with value

Question 4. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−4×2+8x−3f(x)=-4×2+8x-3. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.

Question 5. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

MAT180-HY1 Calculus Assignment Solutions

The function f(x)=8x+2x−1f(x)=8x+2x-1 has one local minimum and one local maximum. This function has a local maximum at x=x= with value and a local minimum at x=x= with value

Question 6. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=(7x+2)e−3xf(x)=(7x+2)e-3x has one critical number. Find it. x =

Question 7. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-54812-4-8-12-16-20

Clear All Draw: Dot

Question 8. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

1234-1-2-3-424-2-4-6-8-10-12-14-16

Clear All Draw: Dot

MAT180-HY1 Calculus Assignment Solutions

Question 9. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph. x4e−x28x4e-x28, 4

12345-1-2-3-4-548121620242832

Clear All Draw: Dot

Question 10. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Find the critical numbers of the function f(x)=−12×5−45×4+80×3+4f(x)=-12×5-45×4+80×3+4 and classify them. x = is a x = is a x = is a

Question 11. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−4×2+10x−7f(x)=-4×2+10x-7. f(x)f(x) has a critical point at x=x= . At the critical point, does f(x)f(x) have a local min, a local max, or neither?

Question 12. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=2×3−36×2+120x+7f(x)=2×3-36×2+120x+7 has one local minimum and one local maximum. This function has a local minimum at xx equals with value and a local maximum at xx equals with value

Question 13. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=2×3−36×2+120x+9f(x)=2×3-36×2+120x+9 has derivative f'(x)=6×2−72x+120f′(x)=6×2-72x+120. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals with value and a local maximum at xx equals with value

MAT180-HY1 Calculus Assignment Solutions

Question 14. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=−2×3+33×2−108x+4f(x)=-2×3+33×2-108x+4 has one local minimum and one local maximum. This function has a local minimum at xx = with value and a local maximum at xx = with value

Question 15. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−4×2+4x−2f(x)=-4×2+4x-2. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.

Question 16. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=(8x−8)e−5xf(x)=(8x-8)e-5x has one critical number. Find it. x =

Question 17. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-5714212835-7-14-21-28

Clear All Draw: Dot

Question 18. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-5-6-12-18-24-30-36-42-48-54-60

Clear All Draw: Dot

Question 19. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph. x1e−x27x1e-x27, 0.4

123-1-2-30.40.81.21.62-0.4-0.8-1.2-1.6-2

Clear All Draw: Dot

MAT180-HY1 Calculus Assignment Solutions

Question 20. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Find the critical numbers of the function f(x)=6×5−15×4−20×3+1f(x)=6×5-15×4-20×3+1 and classify them. x = is a x = is a x = is a

Question 21. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−4×2+6x−2f(x)=-4×2+6x-2. f(x)f(x) has a critical point at x=x= . At the critical point, does f(x)f(x) have a local min, a local max, or neither?

Question 22. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=2×3−27×2+84x+5f(x)=2×3-27×2+84x+5 has one local minimum and one local maximum. This function has a local minimum at xx equals with value and a local maximum at xx equals with value

Question 23. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=2×3−36×2+210x+10f(x)=2×3-36×2+210x+10 has derivative f'(x)=6×2−72x+210f′(x)=6×2-72x+210. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals with value and a local maximum at xx equals with value

Question 24. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=−2×3+33×2−144x+1f(x)=-2×3+33×2-144x+1 has one local minimum and one local maximum. This function has a local minimum at xx = with value and a local maximum at xx = with value

Question 25. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−3×2+8x−1f(x)=-3×2+8x-1. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.

Question 26. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

The function f(x)=(3x−3)e−6xf(x)=(3x-3)e-6x has one critical number. Find it. x =

Question 27. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-54812-4-8-12-16-20

Clear All Draw: Dot

Question 28. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph.

123-1-2-3123456

Clear All Draw: Dot

Question 29. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Mark the critical points on the following graph. x4e−x25x4e-x25, 1

12345-1-2-3-4-51234567891011121314

Clear All Draw: Dot

Question 30. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Find the critical numbers of the function f(x)=12×5−75×4−100×3−5f(x)=12×5-75×4-100×3-5 and classify them. x = is a x = is a x = is a

Question 31. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=−5×2+2x−2f(x)=-5×2+2x-2. f(x)f(x) has a critical point at x=x= . At the critical point, does f(x)f(x) have a local min, a local max, or neither?

MAT180-HY1 Calculus Assignment Solutions

Consider the function f(x)=6√x+4f(x)=6x+4 on the interval [2,6][2,6]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (2,6)(2,6) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.

Question 1. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=4×3−2xf(x)=4×3-2x on the interval [−3,3][-3,3]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one cc in the open interval (−3,3)(-3,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is and the larger one is

Question 2. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=1xf(x)=1x on the interval [1,7][1,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (1,7)(1,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.

Question 3. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=2×3−15×2−36x+10f(x)=2×3-15×2-36x+10 on the interval [−6,7][-6,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (−6,7)(-6,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is and the larger one is

Question 4. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Correct

MAT180-HY1 Calculus Assignment Solutions

Question 5. Last Attempt: 1 out of 1 Score in Gradebook: 1 out of 1

Consider the function f(x)=4×3−4xf(x)=4×3-4x on the interval [−3,3][-3,3]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one cc in the open interval (−3,3)(-3,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is and the larger one is

Question 6. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=7−7x2f(x)=7-7×2 on the interval [−2,3][-2,3]. Find the average or mean slope of the function on this interval, i.e. f(3)−f(−2)3−(−2)=f(3)-f(-2)3-(-2)= By the Mean Value Theorem, we know there exists a cc in the open interval (−2,3)(-2,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.

Question 7. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=2×3−9×2−24x+3f(x)=2×3-9×2-24x+3 on the interval [−5,7][-5,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (−5,7)(-5,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is and the larger one is

Question 8. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=1xf(x)=1x on the interval [4,8][4,8]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (4,8)(4,8) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.

Question 9. Last Attempt: 0 out of 1 Score in Gradebook: 0 out of 1

Consider the function f(x)=8√x+2f(x)=8x+2 on the interval [1,8][1,8]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (1,8)(1,8) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.

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