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In Exercises 63–68, 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 while thinking about the

chain rule.

f'x=3x+1,f0=1

Short Answer

Expert verified

The function isfx=23x+1329+79

Step by step solution

01

Step 1. Given Information

The given derivative isf'x=3x+1,f0=1

02

Step 2. Finding antiderivative

fx=3x+1dxfx=233x+1323+Cfx=23x+1329+C

03

Step 3. Finding the value of C

Given that f0=1

1=29+CC=1-29=79

The function becomerole="math" localid="1649665179684" fx=23x+1329+79

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