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

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Answer 1 · 2018-05-14T11:45:11

#t=2#

First equation:

#x=80t#

Hence,

#t=x/80#

Differentiate,

#dt/dx=1/80#

Second equation:

#y=64t-16t^2#

Differentiate

#dy/dt=64-32t#

Apply chain rule:

#dy/dx=dy/dtxxdt/dx#

Hence,

#dy/dx=(64-32t)(1/80)#

Simplify,

#dy/dx=4/5-2/5t#

When #dy/dx=0#,

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

Simplify,

#2/5t=4/5#

Solve,

#t=2#