Question

Which value of c satisfies the conclusion of the mvt for the function f(x)=7x^2+3x+7 on the interval [-3,3]?

Answer 1

Please see below.

Explanation:

The conclusion of the Mean Value Theorem for `f` on `[a,b]` says:

There is a `c` in `(a,b)` for which `f'(c) = (f(b)-f(a))/(b-a)`.

So, find `f'(x)`, find `(f(b)-f(a))/(b-a)`. Set them equal to each other and solve the equation. Discard any solutions outside `(a,b)`.

I get `c=0`.