Question

How to Find Intervals of Concavity from Second Derivative

Which method is commonly used to determine the intervals of concavity based on the second derivative of a function?

A) Differentiation Rule
B) Critical Point Analysis
C) Second Derivative Test
D) Curve Sketching

Answer 1

The commonly used method to determine the intervals of concavity based on the second derivative of a function is the Second Derivative Test (C).

Step-by-step explanation:

The commonly used method to determine the intervals of concavity based on the second derivative of a function is the Second Derivative Test. The Second Derivative Test states that if the second derivative of a function is positive, then the function is concave upward on that interval, and if the second derivative is negative, then the function is concave downward on that interval. To find the intervals of concavity using this method, you need to evaluate the sign of the second derivative at different points and determine where it changes from positive to negative or from negative to positive.

So, the answer is C.