# The value of the tangent line and derivative of the tangent line at a = 4 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2.6, Problem 20E
To determine

## To find:The value of the tangent line and derivative of the tangent line at a=4 .

Expert Solution

Value of the function and derivative of the function at a=4 are 14 and 4 respectively.

### Explanation of Solution

Given: y=f(x) at (4,3) passes through the point (0,2) .

Let y=f(x) be any function.

It has to find The value of the function and derivative of the function at a=2

m=yy1xx1=3240=14yy1=m(xx1)y3=14(x4)f(x)=y=14x+2f(4)=12(4)+2=3f(4)=limxaf(x)f(a)(xa)=limxa14x+2(f(4))x(4)=limxa14x1x4=limxa14(x4)x4=limxa14=14

Now derivative of the function

f'(x)=4f'(4)=4

Hence, value of the function and derivative of the function at a=4 are 14 and 4 respectively.

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