# The equation of the tangent and the value of a and b ### 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 69E
To determine

## To find:The equation of the tangent and the value of a and b

Expert Solution

The equation of the value a=12,b=2

### Explanation of Solution

Given:

The tangent to the curve

y=ax2

Parallel to the line

2x+y=b

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=ax2.......................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

y=ax2y=2ax........................(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

2x+y=by=2x+by=2.............................(3)

The equation is in slope −intercept form

The slope of the line is =2

From equation (2) and equation (3)

2=2a(2)2=4aa=12

The coordinates of points

y=ax2y=12(22)y=2

Solve for b in the line equation

2(2)+(2)=bb=2

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