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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=xx2+14,f0=0

Short Answer

Expert verified

The function isfx=x2+1510-110

Step by step solution

01

Step 1. Given Information

The given derivative isf'x=xx2+14,f0=0

02

Step 2. Finding antiderivative 

fx=xx2+14dxfx=xt4dt

fx=12t4dtfx=12t55+Cfx=x2+1510+C

03

Step 3. Finding the value of C

Given that f0=0

0+1510+C=0110+C=0C=-110

The function becomefx=x2+1510-110

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