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Chapter 2: Q. 61 (page 222)

In Exercises 59鈥�63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.

f'(x)=xx2+3

Short Answer

Expert verified

The required function is f(x)=12log(x2+3)

Step by step solution

01

Step 1. Given Information  

The given derivative isf'(x)=xx2+3

02

Step 2. Calculation  

We will use a targeted guess and check method to find an antiderivative of given derivative.

ddxf(x)=ddxlog(x2+3)路12=xx2+3

Thus, we get the required function.

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Most popular questions from this chapter

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.

28.f(x)=x4+1,x=2

use the definition of derivative to directly prove the differentiation rules for constant and identity function

Instead of choosing small values of h, we could have chosen values of z close to c. What limit involving z instead of h is equivalent to the one involving h?

Use the definition of the derivative to find f' for each function f in Exercises 39-54

f(x)=-x3-x+1

For each function f(x)and interval [a,b]in 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.

localid="1648369345806" f(x)=x4-2,a,b=1,2.
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