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Chapter 2: Q. 60 (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)=x2ex3

Short Answer

Expert verified

The required function isf(x)=13ex3

Step by step solution

01

Step 1. Given Information  

The given derivative isf'(x)=x2ex3

02

Step 2. Calculation  

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

ddxf(x)=ddx13ex3=13ex3ddx(x3)=13ex33x2=x2ex3

Thus, we get the required function.

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