   Chapter 10.3, Problem 8E

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 2 + 5 t + 4 ,   y   =   4 t   t = 0

To determine

To calculate:

The value of dydx, d2ydx2 slope and concavity of parametric equations x=t2+5t+4,y=4t, at

parameter t=0.

Explanation

Given:

The parametric equations,

x=t2+5t+4y=4t

And, parameter t=0.

Calculation:

Consider the equations,

x=t2+5t+4y=4t

Differentiate x=t2+5t+4 with respect to t, to get,

dxdt=2t+5 …..(1)

Differentiate y=4t with respect to t, to get,

dydt=4 ……(2)

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

dy/dtdx/dt=dydx=42t+5 …..(3)

Now, in order to find slope, substitute t=0 in equation (3).

That is.,

(dydx)t=0=42(0)+5=45

Therefore,

At t=0, slope is 45

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