Question

-Consider the following equation.y = 5(x2 - 4x)(b.). Find.dx/dt.given x = 4, dy/dt = 8.Enter a fraction, integer, or exact decimal. Do not approximate.Submit Answer

Answer 1

The equation is given to be:

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

The derivative of the function is gotten to be:

`(dy)/(dx)=5(2x-4)`

At x = 4, we have:

`\begin{gathered} (dy)/(dx)=5(2\cdot4-4)=5(8-4)=5(4) \\ (dy)/(dx)=20 \end{gathered}`

Recall that:

`(dy)/(dx)=(dy)/(dt)*(dt)/(dx)`

We are given the value of dy/dt to be 8. Therefore, we have:

`20=8\cdot(dt)/(dx)`

We can therefore solve for dx/dt as follows:

`\begin{gathered} (dt)/(dx)=(20)/(8)=(5)/(2) \\ Inversing\text{ }the\text{ }fractions: \\ (dx)/(dt)=(2)/(5) \end{gathered}`

ANSWER

`(dx)/(dt)=(2)/(5)\text{ }or\text{ }0.4`