How do you find the value of t for which (dy/dx)=0 ? .... given x= 80t and y=64t -16 t^2

1 Answer
May 14, 2018

t=2t=2

Explanation:

First equation:

x=80tx=80t

Hence,

t=x/80t=x80

Differentiate,

dt/dx=1/80dtdx=180

Second equation:

y=64t-16t^2y=64t16t2

Differentiate

dy/dt=64-32tdydt=6432t

Apply chain rule:

dy/dx=dy/dtxxdt/dxdydx=dydt×dtdx

Hence,

dy/dx=(64-32t)(1/80)dydx=(6432t)(180)

Simplify,

dy/dx=4/5-2/5tdydx=4525t

When dy/dx=0dydx=0,

4/5-2/5t=04525t=0

Simplify,

2/5t=4/525t=45

Solve,

t=2t=2