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

Answer:

c

Step-by-step 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)

$f'(c)=3+2\sqrt{c}$

Therefore:

$3+2\sqrt{c}=((-119)-(-4))/((49)-(4))$

Simplify:

$3+2\sqrt{c}=-23/9$

$c=81/4$