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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9.4, Problem 42E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 5CP
Problem 6CP
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
BuyFindarrow_forward

Mathematical Applications for the ...

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

The tangent line to a curve at a point closely approximates the curve near the point. In fact, for x-values close enough to the point of tangency, the function and its tangent line are virtually indistinguishable. Problems 41 and 42 explore this relationship. Use each given function and the indicated point to complete the following.

(a) Write the equation of the tangent line to the curve at the indicated point.

(b) Use a graphing calculator to graph both the function and its tangent line. Be sure your graph shows the point of tangency.

(c) Repeatedly zoom in on the point of tangency. Do the function and the tangent line eventually become indistinguishable?

f ( x ) = 4 x − x 2  at  x  = 5

(a)

To determine

To calculate: The equation of the tangent line to curve f(x)=4x−x2 at x=5.

Explanation

Given Information:

The provided function is f(x)=4x−x2 and the provided point is x=5.

Formula Used:

According to sum rule of derivatives,

If f(x)=u(x)+v(x) then f′(x)=u′(x)+v′(x).

According to power rule,

If f(x)=xn then f′(x)=nxn−1.

The equation of tangent at any point (x1,y1) is given by

y−y1=y′(x−x1)

Calculation:

The provided function is f(x)=4x−x2.

The slope of the tangent at any point of the curve is given by derivative of the function.

Therefore, to calculate the slope of the tangent, calculate the derivative of the function.

Apply the sum rule of derivatives,

f(x)=4x−x2f′(x)=ddx(4x−x2)y′=ddx(4x)−ddx(x2)

Use the power rule to find the derivative of the function,

y′=ddx(4x)−ddx(x2)=(4(1)x1−1)+(2x2−1)=4−2x

To determine the slope of the tangent at x=5

(b)

To determine

To graph: The function f(x)=4x−x2 and the tangent line y=−6x+25.

(c)

To determine

If both the curves f(x)=4x−x2 and y=−6x+25 become indistinguishable at x=5.

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Sect-9.1 P-1CPSect-9.1 P-2CPSect-9.1 P-3CPSect-9.1 P-4CPSect-9.1 P-5CPSect-9.1 P-6CPSect-9.1 P-7CPSect-9.1 P-8CPSect-9.1 P-9CPSect-9.1 P-10CP
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The y-coordinate of the center of mass of the region bounded by , x = 1, x = 5, y = 0 is: 4

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

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

For each of the values in the following table, the true value and measured value are given. Determine the absol...

Mathematics For Machine Technology

Solving an Exact Differential Equation In Exercises 714, verify that the differential equation is exact. Then f...

Multivariable Calculus

A process that is in control has a mean of = 12.5 and a standard deviation of = .8. a. Construct the x contro...

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

Describe the differences between a full-text database and one that is not full text, and explain the advantages...

Research Methods for the Behavioral Sciences (MindTap Course List)

Use a graphing calculator to graph each function. fx=logx3

College Algebra (MindTap Course List)

The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. a. What is the point estim...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe some of the problems that can arise when the participants in one treatment condition of a between-subj...

Research Methods for the Behavioral Sciences (MindTap Course List)

Identifying and Sketching a Conic In Exercises 13-22, find the eccentricity and the distance from the pole to t...

Calculus (MindTap Course List)

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