Question

If f(3) = 9 and f '(x) ≥ 2 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

Answer 1

Hmm seems like a mean value problem

Answer 2

\[c \in (a,b) \\ f'(c)=\frac{f(b)-f(a)}{b-a} \\ f'(c)=\frac{f(b)-f(a)}{b-a} \ge 2 \]
input your numbers and solve for f(7)

Answer 3

@nonhacker
Hope that helps
I have to go
peace