MAT 180- Homework 1 Calculus 1

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 .

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

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

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

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.

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