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Chapter 2: Q. 67 (page 234)

Find the function from the given derivative

f鈥�(x)=21鈭�4x2

Short Answer

Expert verified

The function from given derivative is

f(x)=sin鈭�1鈦�(2x)

Step by step solution

01

Step 1.Given information

We have been given derivative function

f鈥�(x)=21鈭�4x2

02

Step 2.Finding the function via approximation 

One can suspecttan-1xfrom the given denominator

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

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Most popular questions from this chapter

For each function f(x)and interval a,bin Exercises 81-86, use the Intermediate Value Theorem to argue that the function must have at least one real root on a,b. Then apply Newton鈥檚 method to approximate that root.

f(x)=x3+1,a,b=-2,1

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

29.f(x)=x12,x=9

Use the definition of the derivative to find f'for each function fin Exercises 34-59

f(x)=3x

For each function f(x)and interval localid="1648297458718" a,bin Exercises localid="1648297462718" 81-86, use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" a,b. Then apply Newton鈥檚 method to approximate that root.

localid="1648297471865" f(x)=x3-3x+1,a,b=1,2

Use the definition of the derivative to find ffor each function fin Exercises 39-54

f(x)=1x2-1
See all solutions

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