   Chapter 3.3, Problem 64E

Chapter
Section
Textbook Problem

# 64-66 Assume that all of the functions are twice differentiable and the second derivatives are never 0.(a) If f and g are concave upward on f, show that f + g is concave upward on I.(b) If f is positive and concave upward on f, show that the function g ( x ) = [ f ( x ) ] 2 is concave upward on I.

To determine

(a)

To show:

f+g is concave upward on I

Explanation

1) Concept:

Concavity test:

If f"(x)>0 then the graph of f is concave upward

2) Given:

f and g are concave upward on I

3) Calculation:

Given that f and g are concave upward on I

By concept

f"(x)>0, g"(x)

To determine

(b)

To show:

The function gx=fx2 is concave upward on I

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