   Chapter 10, Problem 39RE

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 = 1 + 6 t ,       y = 4 − 5 t t = 3

To determine

To calculate: The values of dydx and d2ydx2 and the slope and concavity for the parametric equations: x=1+6t, y=45t and the parameter t=3.

Explanation

Given:

The given parametric equations: x=1+6t, y=45t and the value of the parameter is t=3.

Formula used:

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

Calculation:

The given parametric equations are x=1+6t and y=45t. The formula for differentiation of a function is given as,

dydx=(dydt)(dxdt)

Find the value of dydt,

dydt=ddt(45t)=ddt(4)ddt(5t)=05=5

Similarly, the value of dxdt,

dxdt=ddt(1+6t)=ddt(1)+ddt(6t)=0+6

Now, find the value of dydx

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