   Chapter 10.2, Problem 11E

Chapter
Section
Textbook Problem

# Find dy/dx and d2y/dx2. For which values of t is the curve concave upward?11. x = t2 + 1, y = t2 + t

To determine

To find: The expression of dydx and d2ydx2 for the parametric equations x=t2+1 and y=t2+t , and find the value of t for which the curve is concave upward.

Explanation

Given:

The parametric equation for the variable x is as follows.

x=t2+1 (1)

The parametric equation for the variable y is as follows.

y=t2+t (2)

Calculation:

Differentiate the parametric equation x with respect to t .

x=t2+1dxdt=2t

Differentiate the parametric equation y with respect to t .

y=t2+tdydt=2t+1

Write the chain rule for dydx .

dydx=dydtdxdt

Substitute (2t+1) for dydt and (2t) for dxdt in the above equation.

dydx=(2t+1)(2t)=1+12t

Calculate the second derivative to determine concavity.

d2ydx2=ddt(dydx)dxdt=(1(2t2))2t=14t3

Substitute (1) for t in equation (1)

### 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

#### Find more solutions based on key concepts 