Question

How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0,2] for `f(x) = 2x^2 − 5x + 1`?

Answer 1

Solve `f'(x) = (f(2)-f(0))/(2-0)`. Discard any solutions outside `(0,2)`.

Explanation:

Solve: `4x-5 = -2` so `x = 3/4`

Therefore, `c = 3/4`