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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≤1x3ifx>1

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

Find the derivative

We have

When x≥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≥13x2ifx<1

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