   Chapter 10, Problem 11RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Is the graph of y = x 4 − 3 x 3 + 2 x   − 1 concave up or concave down at x = 2?

To determine

Whether the graph of the equation y=x43x3+2x1 at x=2 is concave up or concave down.

Explanation

Given Information:

The provided equation is y=x43x3+2x1.

Explanation:

Consider the provided equation,

y=x43x3+2x1

Calculate the first derivative of the above equation with respect to x:

y'=4x39x2+2

Differentiate with respect to x again.

y''=12x218x

Now, concavity of f(x) can be found from the sign of f(x). Because f(x) is the first derivative of f(x), wherever the graph of f(x) is increasing, it follows that f(x)>0

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