Answer x intercepts are approximately x = − 2.46 . Local maximum is at approximately ( − 1.15 , 4.04 ) . Local minimum is at approximately ( 1.15 , 0.96 ) . The graph it is very clear that the function is increasing when x < − 1.15 and x > 1.15 and decreasing when − 1.15 < x < 1.15 . Explanation Given information: Given function, f ( x ) = 0.5 x 3 − 2 x + 2.5 Calculation: Consider the function f ( x ) = 0.5 x 3 − 2 x + 2.5 : Input function using key 0.5 X ∧ 3 − 2 X + 2.5 . Adjust the WINDOW and hit GRAPH key. The graph has three x intercepts and 2 turning points. Press 2 n d TRACE to go the CALCULATE menu and highlight the ZERO and press ENTER. When asked for left bound and right bound, move cursor to the left or right of observed zero location. When asked for Guess, simply Hit ENTER key. Therefore, x intercepts are approximately x = − 2.46 . Press 2 n d TRACE to go to the CALCULATE menu and highlight the Maximum and press ENTER. When asked for left bound and right bound, move cursor to the left or right of observed maximum location. When asked for guess, simply hit ENTER key. Therefore, local maximum is at approximately ( − 1.15 , 4.04 ) . Press 2 n d TRACE to go to the CALCULATE menu and highlight the Minimum and press ENTER. When asked for left bound and right bound, move cursor to the left or right of observed maximum location. When asked for guess, simply hit ENTER key. Therefore, local minimum is at approximately ( 1.15 , 0.96 ) . From the graph it is very clear that the function is increasing when x < − 1.15 and x > 1.15 and decreasing when − 1.15 < x < 1.15 .

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Question

Chapter 4.8, Problem 27E

To determine

To sketch: the graph of the function, and to indentify the $x$ intercepts and the points where the local maximums and local minimums occur, to find the intervals for which the function is increasing or decreasing.

Expert Solution & Answer

Answer to Problem 27E

$x$ intercepts are approximately $x=−2.46$ .

Local maximum is at approximately $(−1.15,4.04)$ .

Local minimum is at approximately $(1.15,0.96)$ .

The graph it is very clear that the function is increasing when $x<−1.15$ and $x>1.15$ and decreasing when $−1.15<x<1.15$ .

Explanation of Solution

Given information:

Given function,

$f(x)=0.5x3−2x+2.5$

Calculation:

Consider the function $f(x)=0.5x3−2x+2.5$ :

Input function using key $0.5X∧3−2X+2.5$ .

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 1

Adjust the WINDOW and hit GRAPH key.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 2

The graph has three $x$ intercepts and 2 turning points.

Press 2ⁿ^dTRACE to go the CALCULATE menu and highlight the ZERO and press ENTER.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 3

When asked for left bound and right bound, move cursor to the left or right of observed zero location.

When asked for Guess, simply Hit ENTER key.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 4

Therefore, $x$ intercepts are approximately $x=−2.46$ .

Press 2ⁿ^d TRACE to go to the CALCULATE menu and highlight the Maximum and press ENTER.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 5

When asked for left bound and right bound, move cursor to the left or right of observed maximum location.

When asked for guess, simply hit ENTER key.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 6

Therefore, local maximum is at approximately $(−1.15,4.04)$ .

Press 2ⁿ^d TRACE to go to the CALCULATE menu and highlight the Minimum and press ENTER.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 7

When asked for left bound and right bound, move cursor to the left or right of observed maximum location.

When asked for guess, simply hit ENTER key.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 4.8, Problem 27E , additional homework tip 8

Therefore, local minimum is at approximately $(1.15,0.96)$ .

From the graph it is very clear that the function is increasing when $x<−1.15$ and $x>1.15$ and decreasing when $−1.15<x<1.15$ .

Chapter 4.8, Problem 26E

Chapter 4.8, Problem 28E

Chapter 4 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

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the graph of the function, and to indentify the x intercepts and the points where the local maximums and local minimums occur, to find the intervals for which the function is increasing or decreasing.