# The equation of the tangent ### 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 3.1, Problem 56E
To determine

## To find:The equation of the tangent

Expert Solution

The normal line at x=0 intersect the parabola only once

### Explanation of Solution

Given:

The normal line to the parabola

y=xx2

Concept used:

The equation is in slope −intercept form, y=mx+c

An equation for the line through the point (x1,y1) with slope m is

yy1=m(xx1)

Calculation:

The function

y=xx2.......................(1)

The derivative of a function

y=f(x)y=f(x)=dydx=m

Differentiating the equation (1) with respect to x

y=xx2y=12x........................(2)

The slope of the tangent

m=12(0)m=1

The normal line is perpendicular to the tangent

mnormal=1mtangent=1

An equation for the line through the point (x1,y1) with slope m is

yy1=m(xx1)y1=1(x0)y=1x

The line intersect the parabolas

y=1xy=xx2

Solve through substitution

1x=xx2x22x+1=0(x1)(x1)=0x=1

The normal line at x=0 intersect the parabola only once

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