How do you find the value of c that satisfy the equation $(f(b)-f(a))/(b-a)=f'(c)$ in the conclusion of the mean value theorem for the function $f(x)=4x^2+4x-3$ on the interval [-1,0]#?

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Answer 1 · 2016-12-26T23:10:35

Please see below.

For the problem under consideration, we have

$f(x) = 4x^2+4x-3$

$f'(x) = 8x+4$

$a = -1$ and $b=0$ .

So we need to solve the equation

$f'(x) = (f(0)-f(-1))/(0-(-1))$ on the interval $(-1,0)$

Solve

$8x+4 = (-3-(-3))/(0-(-1))$

$8x+4 = 0$

$x = -1/2$ is in the interval $(-1,0)$ .

So $c = -1/2$ .

How do you find the value of c that satisfy the equation (f(b)-f(a))/(b-a)=f'(c)(f(b)-f(a))/(b-a)=f'(c) in the conclusion of the mean value theorem for the function f(x)=4x^2+4x-3f(x)=4x^2+4x-3 on the interval [-1,0]#?