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Chapter 2: Q. 66 (page 234)

Find the function from its given derivative

f鈥�(x)=2x1鈭�4x2

Short Answer

Expert verified

The function from its given derivative is

f(x)=鈭�121鈭�4x2

Step by step solution

01

Step 1.Given information

WE have been given the derivative of function

f鈥�(x)=2x1鈭�4x2

02

Step 2.We have been finding the function whose derivative is given 

One can suspect thesin鈭�1鈦�xfrom the denominator of function

f(x)=sin鈭�1鈦�(2x)f(x)=sin鈭�1鈦�(2x)f鈥�(x)=11鈭�(2x)2ddx(2x)=21鈭�4x2
03

Step 3.Finding the more appropriate function from previous one 

Now , letting the functionf(x)=鈭�121鈭�4x2

f(x)=鈭�121鈭�4x2f鈥�(x)=鈭�12ddx1鈭�4x212=鈭�12121鈭�4x2鈭�12ddx1鈭�4x2ddxxn=nxn鈭�1=鈭�141鈭�4x2ddx1鈭�ddx4x2=1A1鈭�4x2(A(2x))=鈭�鈭�2x1鈭�4x2=2x1鈭�4x2

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Most popular questions from this chapter

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=(3x+1)3,f(2)=1

The total yearly expenditures by public colleges and universities from 1990 to 2000 can be modeled by the function E(t)=123(1.025)t, where expenditures are measured in billions of dollars and time is measured in years since 1990.

(a) Estimate the total yearly expenditures by these colleges and universities in 1995.

(b) Compute the average rate of change in yearly expenditures between 1990 and 2000.

(c) Compute the average rate of change in yearly expenditures between 1995 and 1996.

(d) Estimate the rate at which yearly expenditures of public colleges and universities were increasing in 1995.

Prove the difference rule in two ways

a) using definition of the derivative

b) using sum and constant multiple rules

Suppose h(t) represents the average height, in feet, of a person who is t years old.

(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?

(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?

(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?

For each function f that follows find all the x-values in the domain of f for which f'(x)=0and all the values for which f'(x)does not exist in later section we will call these values the critical points of f

localid="1648604345877" a)f(x)=x3-2xb)f(x)=x-xc)鈥�f(x)=11+xd)f(x)=x2(x-1)(x-2)2
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