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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.1, Problem 43E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A formula for the derivative of a function f is given. How many critical numbers does f have?

f ′ ( x ) = 1 + 210 sin x x 2 − 6 x + 10

To determine

To find:

Critical numbers for f(x) by using the given  f'(x).

Explanation

1) Concept:

Find the values of x where f'x=0 and f'x doesn’t exist. That gives the critical numbers.

2) Definition:

A critical number of a function f   is a number c in the domain of f  such that either  f'c=0 or f'c does not exist.

3) Given:

 f'(x)=1+210sin⁡xx2-6x+10

4) Calculation:

To find the critical numbers of f(x), find the values of x where f'x=0 and f'x doesn’t exists.

i) Check at which values of x the given f'x doesn’t exist.

f'x will be undefined when the denominator x2-6x+10 is 0. Since x2-6x+10  is not a factorable expression, here we don’t get values of x that makes the denominator zero.

Since we don’t get actual numbers, we need to use a discriminant to see if it has real zeros.

Discriminant = b2-4ac = -62-4*1*10= -4       

Since its negative, it has only imaginary zeros because discriminant b2-4ac≤0, so the quadratic equation has imaginary zeros

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Use Table 12-1 to calculate the future value of the following annuities due. Annuity Payment Time Nominal Inter...

Contemporary Mathematics for Business & Consumers

The graph of x = 2 + 3t, y = 4 − t is a: circle ellipse line parabola

Study Guide for Stewart's Multivariable Calculus, 8th

Horizontal Tangency In Exercises 71 and 72, find the points of horizontal tangency to the polar curve. r=asinco...

Calculus: Early Transcendental Functions (MindTap Course List)

The directrix of the conic given by r=62+10sin is: a) x=53 b) x=35 c) y=53 d) y=35

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercises 1 to 4, state the ratio needed, and use it to find the measure of the indicated line segment to th...

Elementary Geometry for College Students

The following histograms represent the probability distributions of the random variables X and Y. Determine by ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Review In Exercises 71-80, determine the convergence or divergence of the series and identify the test used. n=...

Calculus (MindTap Course List)

Finding Scalar Multiples In Exercises 57 and 58. Find each scalar multiple of v and sketch its graph. v=2,2,1 (...

Multivariable Calculus

Volume and Centroid In Exercises 77 and 78, for the region bounded by the graphs of the equations, find (a) the...

Calculus

Reconsider the sample results in exercise 7. a. Develop an approximate 95 confidence interval for the proportio...

Statistics for Business & Economics, Revised (MindTap Course List)

Each year the College Board publishes a profile of students taking the SAT. In the report 2016 College Bound Se...

Introduction To Statistics And Data Analysis

A recent survey showed that a majority of Americans plan on doing their holiday shoppingonline because they don...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Two sides and an angle opposite one of the sides of triangles are given in the following exercises. Identify ea...

Mathematics For Machine Technology

Explain why partial counterbalancing is sometimes necessary.

Research Methods for the Behavioral Sciences (MindTap Course List)

A researcher examines the relationship between the quality of breakfast and academic performance for a group of...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find the inverse of each one-to-one function and graph both the function and its inverse on the same set of coo...

College Algebra (MindTap Course List)

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