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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=5x2+142x,f1=25

Short Answer

Expert verified

The function isfx=x2+15-7

Step by step solution

01

Step 1. Given Information

The given derivative isf'x=5x2+142x,f1=25

02

Step 2. Finding antiderivative

fx=5x2+142xdxfx=5t42xdt2x=5t4dtfx=5t55+Cfx=t5+Cfx=x2+15+C

03

Step 3. Finding the value of C

Given that f1=25

1+15+C=2532+C=25C=25-32=-7

The function becomefx=x2+15-7

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