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Chapter 2: Q. 62 (page 222)

In Exercises 59鈥�63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.

f'(x)=ex(1+ex)

Short Answer

Expert verified

The required function is f(x)=ex+e2x2

Step by step solution

01

Step 1. Given Information  

The given derivative isf'(x)=ex(1+ex)

02

Step 2. Calculation  

We will use a targeted guess and check method to find an antiderivative of given derivative.

ddxf(x)=ddxex+e2x2=ex+e2x2路2=ex+e2x=ex(1+ex)

Thus, we get the required function.

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Most popular questions from this chapter

In the text we noted that if f(u(v(x))) was a composition of three functions, then its derivative is dfdx=dfdu脳dudv脳dvdx. Write this rule in 鈥減rime鈥� notation.

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

f'(x)=(x4-8)(1-3x5);f(0)=2

use the definition of derivative to directly prove the differentiation rules for constant and identity function

Use the definition of the derivative to find f'for each function fin Exercises 39-54

role="math" localid="1648290170541" f(x)=x-1x+3

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
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