   Chapter 10, Problem 40RE

Chapter
Section
Textbook Problem

# Finding Slope and Concavity In Exercises 39 - 46. find dy/dx and d 2 y / d x 2 , and find the slope and concavity (if possible) at the given value of the parameter.Parametric Equations Parameter x = t − 6 ,       y = t 2 t = 5

To determine

To calculate: The values of dydx and d2ydx2 and the slope and concavity for the parametric equations: x=t6, y=t2 and the parameter t=5.

Explanation

Given:

The given parametric equations: x=t6, y=t2 and the parameter is t=5.

Formula used:

Differentiation of a parametric function is given by dydx=(dydt)(dxdt).

Calculation:

The given parametric equations are x=t6 and y=t2.

Differentiation of the parametric equations as,

dydt=ddt(t2)=2t21=2t

And,

dxdt=ddt(t6)=ddt(t)ddt(6)=1

Now find the value of dydx,

dydx=

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