Optimization

Question

Suppose f(0) = 3 and 2 is less than f '(x) which is less than 4 for all x in the interval [-5; 5]. Determine the greatest and least possible values of f(2).

Answer 1

f(2) = f(0) + 2c, where c is some value between 2 and 4 because f' is between 2 and 4 in this interval (a subset of [-5, 5].)

f(0) = 3.

Thus, f(2) is between 3 + 2*2 and 3 +2*4, or 7 and 11.