# The equation of the tangent and parallel to the line

### 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 67E
To determine

Expert Solution

## Answer to Problem 67E

The equation of the line is m=23

### Explanation of Solution

Given:

The tangent to the curve

y=ax3+bx2+cx+d

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=ax3+bx2+cx+d.......................(1)

The derivative of a function

y=f(x)y=f(x)=dydx=m=x2x1y2y1

Differentiating the equation (1) with respect to x

y=ax3+bx2+cx+dy=3ax2+2bx+c........................(2)

The derivative is slope of the tangent line so in order to the slope of the tangent line

The derivative of constant is zero

m=x2x1y2y1m=2260m=46m=23..............................(3)

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