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 65E
To determine

To find:

The equation of the parabola

Expert Solution

Answer to Problem 65E

The equation of the parabola is y=2x2x

Explanation of Solution

Given:

The normal line to the parabola

  y=ax2+bx

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+bx.......................(1)

The derivative of a function

  y=f(x)y=f(x)=dydx=m

Differentiating the equation (1) with respect to x

  y=ax2+bxy=2ax+b........................(2)

The slope of the tangent

  m=2a(1)+bm=2a+b

Point (1,1) is a point on the parabola

So, satisfies the original parabola equation

  1=a(1)2+b(1)a+b=1

The line intersect the parabolas

  2a+b=3a+b=1solvea=2a+b=1b=1

So parabola equation is

  y=ax2+bxy=2x2x

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!