Supposef (0) = 2 and 2 ≤ f ' (x) ≤ 7for all x in the interval [-5, 5]. determine the greatest and least possible values of f (2). least

If the slope of the function is 2, the amount it can change over the interval 0-2 is

... 2*2 = 4 units

If the slope is 7, the amount it can change over the interval 0-2 is

... 2*7 = 14 units

The least possible value of f (2) is 2+4 = 6.

The greatest possible value of f (2) is 2+14 = 16.