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 3.1, Problem 30E
To determine

To find:

The equation of the tangent line to the curve at the given point

Expert Solution

Answer to Problem 30E

The equation of the tangent line is y=4(1+2x)(x1)+9

Explanation of Solution

Given:

The function is

  f(x)=(1+2x)2

Concept used:

An equation of a line l through a point P1(x1,y1) with slope m . If P(x,y) is any point with xx1

Then P is on l if and only if the slope of the line through P1 and P

The equation is yy1=m(xx1)

Calculation:

The function

  f(x)=(1+2x)2...................(1)

The derivative of a function

  y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

  dydx=ddx(1+2x)2dydx=2(1+2x)2dydx=4(1+2x)

The point is (1,9)

The equation is

  yy1=m(xx1)y9=4(1+2x)(x1)y=4(1+2x)(x1)+9

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!