BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.6, Problem 24E
To determine

To find:The equation of the tangent line and derivative of the tangent line at a=1 .

Expert Solution

Answer to Problem 24E

The tangent line is y=4x5 and g'(1)=4 .

Explanation of Solution

Given: g(x)=x42 be any curve.

Concept used: g'(a)=limxa[g(x)g(a)]xa

Let g(x)=x42 be anygiven function.

It has to find equation of the tangent line and derivative of the tangent line at a=1 .

Therefore

  g'(a)=limxa[g(x)g(a)]xa

  g'(1)=limx1[g(x)g(1)]x1g'(1)=limx1[(x42)(142)]x1g'(1)=limx1(x41)x1g'(1)=limx1(x21)(x2+1)x1g'(1)=limx1(x1)(x2+1)(x+1)x1g'(1)=limx1(x2+1)(x+1)g'(1)=(12+1)(1+1)=4

So, the slope of the line at (1,1) is 4 .

Therefore the equation of the tangent is

  y(1)x1=4y+1x1=4y+1=4(x1)y+1=4x4y=4x5

Hence, the tangent line is y=4x5 .

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