Question

a function f satisfies the following conditions: f(5)=20, f'(5)=2, and f"(x)<0, for x>=5. which of the following are possible values for f(7)? possible choices are 28, 20, 26, 24, 22

Answer 1

So the first derivative at f(5) is 2, meaning that if the acceleration was constant (f''(x) = 0), we could assume f(5) = 20, f(6) = 22, f(7) = 24. However, it tells you that f''(x) < 0, which means it is negative. It has a positive velocity, which means f(7) must be greater than 20. But since it has a negative acceleration, f(7) must be less than 24, leaving 22 as the only answer.