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:

$\frac{dy}{dx}=5(2x-4)$

At x = 4, we have:

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

Recall that:

$\frac{dy}{dx}=\frac{dy}{dt}\times\frac{dt}{dx}$

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

$20=8\cdot\frac{dt}{dx}$

We can therefore solve for dx/dt as follows:

$\begin{gathered} \frac{dt}{dx}=\frac{20}{8}=\frac{5}{2} \\ Inversing\text{ }the\text{ }fractions: \\ \frac{dx}{dt}=\frac{2}{5} \end{gathered}$

ANSWER

$\frac{dx}{dt}=\frac{2}{5}\text{ }or\text{ }0.4$