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Chapter 2: Q. 64 (page 210)

In Exercises 63鈥�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=鈭�5x2+142xdxfx=鈭�5t42xdt2x=5鈭�t4dtfx=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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Most popular questions from this chapter

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 it may be helpful to do some preliminary algebra

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