   Chapter 10, Problem 1RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.1. If the parametric curve x = f(t), y = g(t) satisfies g′(1) = 0, then it has a horizontal tangent when t = 1.

To determine

To find: Whether the given statement is true or false, and explain with an example if necessary to prove your answer.

Explanation

Given:

The parametric equation of the variable x is as follows.

x=f(t)

The parametric equation of the variable y is as follows.

y=g(t)

Here the first derivative of g(t) at 1 for t g'(1) is 0.

Calculation:

Consider an example and assume values for the given equation as follows.

x=f(t)=(t1)3 (1)

y=g(t)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 