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Chapter 2: Q 30 (page 155)

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

f'x=3x2x3+1,f2=6

Short Answer

Expert verified

The anti derivative isfx=2x3+1

Step by step solution

01

Step 1:The given information 

The given expression isf'x=3x2x3+1

02

Step 2:Simplification

Given

f'x=3x2x3+1

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

Here 3x2is a derivative of x3+1

Now The given function is in the power -12,therefore it must be derivative of a sqaure root function

Hence fx=2x3+1+c

Now,

f2=6

鈬�6=223+1+c鈬�6=29+c鈬�6=6+c

鈬�c=0

Therefore

fx=2x3+1

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Most popular questions from this chapter

In Exercises 69鈥�80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

fx=x2-3,ifx<3x+2,ifx鈮�3,x=3

Find the derivative of the absolute value function and piecewise defined function

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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=2 seconds, with h=0.1,h=0.01h=-0.1andh=-0.01

Use the differentiation rules developed in this section to find

the derivatives of the functions

f(x)=4-x7

For each function f(x)and interval localid="1648297458718" a,bin Exercises localid="1648297462718" 81-86, use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" a,b. Then apply Newton鈥檚 method to approximate that root.

localid="1648297471865" f(x)=x3-3x+1,a,b=1,2
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