   Chapter 10.2, Problem 13E

Chapter
Section
Textbook Problem

# Find dy/dx and d2y/dx2. For which values of t is the curve concave upward?13. x = et, y = te−t

To determine

To find: the value of dydx and d2ydx2 for the parametric equations x=et and y=tet and find for value of t , whether the curve is concave upward.

Explanation

Given:

The parametric equation for the variable x is as follows.

x=et (1)

The parametric equation for the variable y is as follows.

y=tet (2)

Calculation:

Differentiate the parametric equation x with respect to t .

x=etdxdt=et

Differentiate the parametric equation y with respect to t .

dydt=ddt(tet)=tet+et=et(1t)

Write the chain rule for dydx .

dydx=dydtdxdt

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

dydx=(et(1t))(et)=e2t(1t)

Calculate the second derivative to determine concavity.

d2ydx2=ddt(dydx)dxdt=e2t(1)+(1t)(2e2t)et=e2t(12+2t)et=e3t(2t3)

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

#### In Exercises 47-52, find and simplify f(a+h)f(a)h(h0) for each function. 51. f(x)=1x

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Elementary Technical Mathematics

#### The normal plane to at t = 1 has equation:

Study Guide for Stewart's Multivariable Calculus, 8th

#### limx(12)x2= a) 0 b) 1 c) d) does not exist

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

#### Graph each function. fx=x2-4

College Algebra (MindTap Course List) 