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 18E
To determine

To find:The equation of the tangent line of the given graph.

Expert Solution

Answer to Problem 18E

  y=4x23 be the equation of the tangent line.

Explanation of Solution

Given: y=g(x) at x=5 if g(5)=3 and g'(5)=4

Concept used:

Tangent of line: y=mx+c

Let y=mx+c be the tangent line.

It has to find equation of the tangent line it means value of m and c

Here g(5)=3 and g'(5)=4 is given

Now

  y=mx+c

  g(x)=mx+cg'(x)=m(1)

  3=m(5)+c         [g(5)=3]5m+c=3        (2)

  m=4    [g'(5)=4]

Put the value of m=4 in equation (2) .

  5m+c=3 

  5(4)+c=3 20+c=3 c=23 

Hence, y=4x23 be the equation of the tangent line.

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