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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=-6xx2+14,f0=1

Short Answer

Expert verified

The function isfx=-35x2+15+85

Step by step solution

01

Step 1. Given Information

The given derivative isf'x=-6xx2+14,f0=1

02

Step 2. Finding antiderivative

fx=-6xx2+14dxfx=-6xt4dt2xfx=-3t4dtfx=-3t55+Cfx=-35x2+15+C

03

Step 3. Finding the value of C

Given that f0=1

-350+15+C=1-35+C=1C=1+35=85

The function becomefx=-35x2+15+85

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