Question

Determine if the function f(x) = 4√x − 3x satisfies the Mean Value Theorem on [4, 49]. If so, find all numbers c on the interval that satisfy the theorem.

a) c = 812b) c = −814c) c = 818d) c = 814

Answer 1

c

Explanation:

The mean value theorem states that for a continuous and differentiable function on a interval there exists a number c from that interval, that

`f'(c)=(f(b)-f(a))/(b-a)`

First we must determine the endpoints:

`f(49)=-119`

`f(4)=-4`

We find the derivative of the function, f'(c)

`f'(c)=3+2√(c)`

Therefore:

`3+2√(c)=((-119)-(-4))/((49)-(4))`

Simplify:

`3+2√(c)=-23/9`

`c=81/4`