   Chapter 10.1, Problem 22E ### 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

# For each function and graph in Problems 21-24(a) use the graph to identify x -values for which y' > 0, y’ < 0, y' = 0, and y’ does not exist.(b) use the derivative to check your conclusions. y = 1 2 x 2 − 4 x + 1 (a)

To determine

The x-values where y>0,y<0 and y=0 for the function y=12x24x+1 using the graph: Explanation

Given Information:

The provided equation is y=12x24x+1.

Explanation:

Consider the provided graph:

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval.

As per the First Derivative Test,

The first derivative of the function is evaluated. The first derivative is made equal to zero in order to get the critical points.

The values of the critical values are kept inside the original function which gives the critical points, that is x=4.

Thus, x=4 if y=0

Now, check the graph on left and right of x=4

On the left of x=4, graph is increasing, so y

(b)

To determine

To calculate: The conclusions from the derivative where the function y=12x24x+1.

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