Does the function satisfy the hypotheses of the Mean Value Theorem on the given

Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

f(x) = 3x2 5x + 2,    [0, 2]

Yes, it does not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem.

No, f is not continuous on [0, 2].

No, f is continuous on [0, 2] but not differentiable on (0, 2).

There is not enough information to verify if this function satifies the Mean Value Theorem.

If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE).

c =

Explanation / Answer

The function is continuous and differentiable on the interval, so it satisifes the MVT.

Plug the points in to get the coordinates.
f(0)=2
f(2)=4

Find the slope between these two points.

(2)-(4)/(0-2)= 1

Find the derivative of the function. f(x)=3x2 5x + 2

f'(x)=6x-5

Set these two things equal.
1=6x-5

c=1

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.