Question

Suppose that SSa where a b and c are positive real numbers. Given that f′(x)>0 for interval (a,b) and f′(x)<0 for interval (b,c) A. Would f(b) be a local extreme? Explair your answer: B. Is there enough information to canclude that f(b) is a global extreme? Explain your answer.

Answer 1

A. No, f(b) would not be a local extreme. B. No, there is not enough information to conclude that f(b) is a global extreme.

Step-by-step explanation:

A. No, f(b) would not be a local extreme. A local extreme occurs when the derivative changes sign from positive to negative or vice versa. Since f′(x)>0 before b and f′(x)<0 after b, there is no change in sign and therefore no local extreme at b.

B. No, there is not enough information to conclude that f(b) is a global extreme. To determine global extrema, we need to know the behavior of the function beyond the given intervals (a,b) and (b,c).

Learn more about Local and Global Extrema