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High School Math Calculus CALCULUS-W/XL ACCESS

The numerical derivative of the function and also find it is differentiable or not.

The numerical derivative of the function and also find it is differentiable or not.

Solution Summary: The author calculates the numerical derivative of the function and also finds it is differentiable or not.

CALCULUS-W/XL ACCESS

CALCULUS-W/XL ACCESS

6th Edition

ISBN: 9781418300197

Author: Finney

Publisher: PEARSON

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Question

Chapter 2.2, Problem 21E

To determine

To calculate: The numerical derivative of the function and also find it is differentiable or not.

Expert Solution & Answer

Answer to Problem 21E

The numerical derivative is −3.9999 and differentiable at the indicated value.

Explanation of Solution

Given information:

The function is fx=x3−4x , x=−2 , h=0.001 .

Concept used:

The formula used to find the numerical derivative is NDERfx,a=fx+h−fx−h2h

Calculation:

The function is fx=x3−4x .

Substitute the values in the formula NDERfx,a=fx+h−fx−h2h .

NDERx3−4x,a=a+0.0013−4a+0.001−a−0.0013+4a−0.0012×0.001

Substitute the value of 0 for a in the above formula.

NDERx3−4x,−2=−2+0.0013−4−2+0.001−−2−0.0013+4−2−0.0012×0.001=−7.988005999+7.996+8.012006001−8.0040.002=0.0160000020.002=8.000001

Check for differentiability.

Left hand derivative at x=−2 .

limh→0f−2−h−f−2−h=limh→0−2−h3−4−2−h−−23−4−2−h=limh→0−8−h3−12h−6h2+8+4h+8−8−h=limh→0−hh2+6h+8−h=8

Right hand derivative at x=−2 .

limh→0f−2+h−f−2h=limh→0−2+h3−4−2+h−−23−4−2h=limh→0−8+h3+12h−6h2−8−4h+8−8h=limh→0hh2−6h+8h=8

Since the right derivative and left hand derivative are equal.

Conclusion: The numerical derivative of the function is 8.000001 and it is differentiable at x=−2 .

Chapter 2.2, Problem 20E

Chapter 2.2, Problem 22E

Chapter 2 Solutions

CALCULUS-W/XL ACCESS

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