Question

Find the number c that satisfies the conclusion of the Mean Value Theorem.

f(x) = 3x^2 + 2x + 1

[-1, 1]

Answer 1

According to the& Mean Value Theorem,
f'(c) = (f(b) - f(a))/(b-a) = (f(1) - f(-1))/(1-(-1)) = 4/2 = 2
f'(c) = 6c + 2 = 2

c = 0