Let f(14) = 5 and f'(2) > 3 for 14 < I< 20. How small can f(20) be? By the Mean Value Theorem, for some c E (14, 20)
f'(c)
20 - 14
of'(c)(20 - 14)
Of(c)(20 - 14)
f(c)
20 - 14
F(20) - f(14) =
Replacing f(14) by its value, we get f(20)
Since f'(2) >3, we have f(20) >
this the smallest f(20) can be.