Question

Describe the graph of f at the given point relative to the existence of a local maximum or minimum. Assume that f(x) is continuous on (-infinity,infinity).
(9,f(9)) if f'(9)=0 and f''(9)<0

What is the best description of the graph of f at the point (9,f(9))?

A) Unable to determine from the given information
B) Neither
C) Local Maximum
D) Local Minimum

Answer 1

Because the second derivative of the function at the point is negative, the graph must be concave down at this point. Because the first derivative indicates that the function is also likely to be a maximum or minimum, the point must be a maximum.