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Chapter 2: Q. 72 (page 198)

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

f(x)=3x+1ifx鈮�1x3ifx>1

Short Answer

Expert verified

The derivative of the piecewise function isf'(x)=3ifx鈮�13x2ifx<1

Step by step solution

01

Given information

We are given A functionf(x)=3x+1ifx鈮�1x3ifx>1

02

Find the derivative

We have

When x鈮�1

f(x)=3x+1

Then f'(x)=3

When x<1

f(x)=x3f'(x)=3x2

Now we have to check the derivative at 1

As the value of the left hand limit is equal to the right hand limit the function is continuous

Now,

We calculate the value of both the derivatives at 1

We get it as 3 for both the cases

Hence the function is differentiable at x=1

Hence

f'(x)=3ifx鈮�13x2ifx<1

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Most popular questions from this chapter

For each function graphed 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.

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)=(3x+1)3,f(2)=1

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a) using definition of the derivative

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