Chapter 10.3, Problem 98E

### 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

# True or False? In Exercises 97-100, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The curve given by x = t 3 and y = t 2 has a horizontal tangent at the origin because d y / d t = 0 when t = 0

To determine
The statement “The curve given by x=t3 and y=t2 has a horizontal tangent at the origin because dydt=0 at point t=0” is true or false.

Explanation

Consider the equations,

x=t3y=t2

Differentiate x=t3 with respect to t, to get,

dxdt=3t2

Differentiate y=t2 with respect to t, to get,

dydt=2t

The Curve will have horizontal tangent if, dydt=0 and dxdtâ‰ 0 at point t=t0

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