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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.1, Problem 41E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Interpreting a Graph In Exercises 39–42, the graph of the derivative of a function is given. Sketch the graphs of two functions that have the given derivative. (There is more than one correct answer.)

Chapter 5.1, Problem 41E, Interpreting a Graph In Exercises 3942, the graph of the derivative of a function is given. Sketch

To determine

To graph: The two functions of the derivative whose graph is shown by,

Calculus: An Applied Approach (MindTap Course List), Chapter 5.1, Problem 41E

Explanation

Given Information:

The graph of the provided derivative is shown below.

Graph:

From the graph, there is a straight line passes through origin and for positive value of x the corresponding value of derivative function is positive while for negative values of x the corresponding value of derivative function is negative.

So, the derivative function is given as,

f′(x)=x

Integrate the above derivative function use the basic rule of integration ∫xndx=xn+1n+1+C.

∫f′(x)dx=∫xdxf(x)=x1+11+1+C=x22+C

The value of C is any constant. It can by any numerical value.

Substitute 0 for C in above function.

f(x)=x22+0=x22

Substitute 2 for C in above function.

f(x)=x22+2

Therefore, the function for that derivative is (f′(x)=x) are f(x)=x22 or f(x)=x22+2.

Graph the function f(x)=x22. It is quadratic function so the graph of this function is parabola.

Now, choose some values for x and compute the value for f(x), in order to form the ordered pairs that will plot on the graph.

So, put x=−2 in the function f(x)=x22.

f(−2)=(−2)22=42=2

Now, put x=0 in the function f(x)=x22,

f(0)=(0)22=0

Now, put x=2 in the function f(x)=x22,

f(2)=(2)22=42=2

The required table is shown below,

x

f(x)

(x,f(x))

−2

2

(−2,2)

0

0

(0,0)

2

2

(2,2)

Therefore, the graph of the function f(x)=x22 as shown below,

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Research Methods for the Behavioral Sciences (MindTap Course List)

Explain why logbln1 is undefined.

College Algebra (MindTap Course List)

The article Cops Get Screened for Digital Dirt (USA TODAY, November 12, 2010) summarizes a report of law enforc...

Introduction To Statistics And Data Analysis

Define the reliability of measurement and explain why and how it is measured.

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the arc length ABC if r=5.75in. and ABC=85.5 . Round the answer to 2 decimal places.

Mathematics For Machine Technology

Winter visitors are extremely important to the economy of Southwest Florida. Hotel occupancy is an often-report...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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