If f(1) = 3 and f '(x) ≥ 2 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Question

If f(1) = 3 and f '(x) ≥ 2 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Answer 1

Secant line:

B = y - mx = 3 - 2*1 = 1

secant line is y=2x+1

at x=6, y=13

function must be at least 13