Question

How do you find all numbers c that satisfies the conclusion of the Mean Value Theorem for the function `f(x)=9x^2+6x+4` in the interval [-1,1]?

Answer 1

Solve `f'(x) = (f(1)-f(-1))/(1-(-1))` keep only solutions in `(-1,1)`.

Explanation:

`18x+6 = 6` has solution `x=0`, so the only number `c` that satisfies the conclusion of MVT for this function on this interval is `c=0`.