   Chapter 10.3, Problem 42E

Chapter
Section
Textbook Problem

# Determining Concavity In Exercises 43-48, determine the open t-intervals on which the curve is concave downward or concave upward. x = t 2 ,   y = ln t

To determine

To calculate: The open t-interval on which the curve of parametric equations, x=t2,y=lnt is

concave downward or concave upward.

Explanation

Given:

The parametric equation,

x=t2y=lnt

Formula used:

If d2ydx2>0, then the curve is concave up and if d2ydx2<0, then the curve is concave downward.

Calculation:

Consider the equations,

x=t2y=lnt

Differentiate x=t2 with respect to t,

dxdt=2t...... (1)

Differentiate y=lnt with respect to t,

dydt=1t...... (2)

Divide equation (2) by (1),

dydx=dydtdxdt=1t2t=

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 