Question #1864

Find the number c that satisfies the conclusion of the Mean Value Theorem.
f(x) = 3x^2 + 2x + 1
[-1, 1]

Expert's answer

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

f'(c) = (f(b) - f(a))/(b-a) = (f(1) - f(-1))/(1-(-1)) = 4/2 = 2

f'(c) = 6c + 2 = 2

c = 0

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