/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q36. Determine whether each function ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q36. (page 291)

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=4x-x2+1

Short Answer

Expert verified

The function has maximum value that is 5.

Step by step solution

01

Step 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a鈮�0, the x-coordinate of vertex is -b2a.

The graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
02

Step 2. Given Information.

The given function is f(x)=4x-x2+1=-x2+4x+1

03

Step 3. Solution.

In the function f(x)=-x2+4x+1, we have a=-1,b=4,c=1

Here, a=-1<0

So, the graph opens down and has a maximum value.

The maximum value of the function is the y-coordinate of the vertex.

Thex-coordinate of the vertex is

鈭�b2a=鈭�42(鈭�1)..........a=鈭�1,b=4=2

Find they-coordinate of the vertex by evaluating the function for x=2.

f(2)=-22+42+1=5

So, the maximum value of function is 5.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

x2-3x=0

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=3x2+6x-1

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=3x2

Give an example of a quadratic function. Identify its quadratic term, linear term, and constant term.

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-4x+4
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.