   Chapter 10.3, Problem 7E

Chapter
Section
Textbook Problem

# Finding Slope and Concavity In Exercises 9-18, find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter.Parametric Equations Parameter x = t + 1 ,   y   =   t 2 + 3 t t = − 2

To determine

To calculate:

The value of dydx, d2ydx2 slope and concavity of parametric equations x=t+1,y=t2+3t, at

parameter t=2.

Explanation

Given:

The parametric equations,

x=t+1y=t2+3t

And, parameter t=2.

Calculation:

Consider the equations,

x=t+1y=t2+3t

Differentiate x=t+1 with respect to t, to get,

dxdt=1 ….. (1)

Differentiate y=t2+3t with respect to t, to get,

dydt=2t+3 …… (2)

Divide equation (1) by (2), to get,

dy/dtdx/dt=dydx=2t+31 ...... (3)

Now, in order to find slope, substitute t=2 in equation (3).

That is

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