Suppose the function d(t) is differentiable for all real numbers. Which of the following statements proves the

Suppose the function d(t) is differentiable for all real numbers. Which of the following statements proves there is a relative maximum at t = 3?
a. d ' < 0 when t < 3 and d ' > 0 when t > 3
b. d ' > 0 when t < 3 and d ' < 0 when t > 3
c. d ' = 0 and d " = 0 when t = 3
d. d ' = 0 and d " ≠ 0 when t = 3

a) This shows that at t = 3 is a min.
b) A consequence of the first derivative test, this shows at t = 3 is a max
c) This shows that t = 3 is an infection point
d) This is impossible

Hence (b) is correct

Yin