17 Nov 2021
Problem 36d
Page 280
Section 4.3: Derivatives and Shapes of Curves
Chapter 4: Applications of Differentiation
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17 Nov 2021
Given information
Given the function is .
The main objective is to find the intervals of concavity and the inflection points.
Concavity:
The function is concave upward in an interval if on that interval.
The function is concave downward in an interval if on that interval.
The inflection point is defined as the point at which the concavity of the function changes from up to down or down to up.
Step-by-step explanation
Step 1.
Find :
Solving one can get real solutions and .
So, the function is concave up in the interval .