Chapter 10.3, Problem 36E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Horizontal and Vertical Tangency In Exercises 35-42, find all points (if any) of horizontal and vertical tangency to the curse. Use a graphing utility to confirm your results. x = t 2 − t + 2 ,     y = t 3 − 3 t

To determine
All the points of horizontal & vertical tangency to the curve and verify the result by the use of graphing utility.

Explanation

a) Given:

x=t2âˆ’t+2....(1)y=t3âˆ’3t......(2)

b) Calculation:

Differentiate both the functions with respect to t,

dxdt=2tâˆ’1 & dydt=3t2âˆ’3

For horizontal tangency equate dydt=0,

âˆ´3t2âˆ’3=0.

âˆ´t=Â±1

Now, substitute t=Â±1 in both the equations,

x=12âˆ’1+2....(1)y=13âˆ’3(1)......(2).

x=(âˆ’1)2âˆ’(âˆ’1)+2

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