Question

Consider the following equation.-y = 5(x2 - 4x)(a) Find dy/dt, given x = 2, dx/dt = 2.(b) Find dx/dt, given x = 4, dy/dt = 8.

Answer 1

The given function is:

`y=5(x^2-4x)`

Therefore,

`\begin{gathered} (dy)/(dx)=5(2x-4) \\ (dy)/(dx)=10(x-2) \end{gathered}`

Recall that:

`\begin{gathered} (dy)/(dt)=(dy)/(dx)\cdot(dx)/(dt) \\ \text{ Substitute }(dy)/(dx)=10(x-2)\text{ into the equation:} \\ (dy)/(dt)=10(dx)/(dt)(x-2) \end{gathered}`

Substitute x = 2 and dx/dt = 2

`(dy)/(dt)=10(2-2)\cdot2=0`

Next, Substitute x = 4 and dy/dt = 8 into the equation:

`\begin{gathered} 8=10(dx)/(dt)(4-2) \\ 20(dx)/(dt)=8 \\ (dx)/(dt)=(2)/(5) \end{gathered}`

(a) dy/dt = 0

(b) dx/dt = 2/5