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Chapter 2: Q 36 (page 238)

Find a function fthat has the given derivative f' and value f(c).

f'x=11-4x2,f0=0

Short Answer

Expert verified

The anti derivative isfx=12tanh-12x

Step by step solution

01

Step 1:Given information

The given expression isf'x=11-4x2,f0=0

02

Step 2:Simplification

Given

f'x=11-4x2

We will use an intelligent guess-and-check method to find f

Since differentiating a power function one and derivative of tanh-1xis

11-x2

One can start with fx=tanh-1(2x)

f'x=ddxtanh-12x

=11-4x2ddx2x

=21-4x2

Hence, we can guess the function as

fx=12tanh-12x+c

Now, given f0=0

鈬�0=tanh-10+c

鈬�c=0

Therefore

fx=12tanh-12x

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Most popular questions from this chapter

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