Using the Mean Value Theorem, how small can f(10) be, given the conditions below? f(2)=20 and f'(x)≥9 for 2

Question

Using the Mean Value Theorem, how small can f(10) be, given the conditions below? f(2)=20 and f'(x)≥9 for 2<x<10

Yefim S. · Accepted Answer

f(10) - f(2) = f'(x)·(10 - 2) ≥ 9·8; f(10) ≥ 72 + 20 = 92; So, smallest value of f(10) is 92

Using the Mean Value Theorem, how small can f(10) be, given the conditions below? f(2)=20 and f'(x)≥9 for 2<x<10