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Chapter 2: Q 33 (page 238)

Find a function f that has the given derivative f' and value f(c).

f'x=11+4x,f0=1

Short Answer

Expert verified

The antiderivative isf(x)=log(1+4x)+1

Step by step solution

01

Step 1:Given information

The given expression isf'x=11+4x,f0=1

02

Step 2:Simplificaion

Given f'x=11+4x

We will use an intelligent guess-and-check method to find f

here 1xis the derivative of logxwherelogx=1+4x

Therefore 11+4xis the derivative of log1+4x

hence,

fx=log1+4x+c

now,

f0=1⇒1=log1+0+c⇒c=1

Therefore antiderivative isf(x)=log(1+4x)+1

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Most popular questions from this chapter

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

After t=1 seconds, with h=0.5,h=0.25,h=-0.5andh=-0.2

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