Which value of c satisfies the conclusion of the MVT for the function f(x) = 7x2 + 7x + 6 on the interval [−7, 9]?

Answer 1

f(x) = 7x² + 7x + 6 is continuous on [-7,9] and is differentiable on (-7,9).

By the Mean Value Theorem, there is at least one number,c, in the interval (-7,9) such that

f'(c) = [f(9) - f(-7)] / (9 - (-7)).

So, 14c + 7 = 21

14c = 14

c = 1