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
Multiply: 37⋅101137⋅1011 Enter your answer as a single, reduced fraction
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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