The curve C has the parametric equations x=4t+3 and y+ 4t +8 +5/(2t). Find the value of dy/dx at the point on curve C where t=2.

a) What can we find from what we have been given?

dx/dt and dy/dt

How can we relate these values to dy/dx?

In the context of equations that only contain two variables, their derivatives behave like fractions. The only equations that one would come across in C4 are equations containing two variables.

Just like 2/5 = 3/5 / 3/2 

dy/dx = dy/dt / dx/dt
 

So firstly find dx/dt and dy/dt

dx/dt = 4

dy/dt = 4 -(5/2)t^-2

Now

dy/dx= (4-(5/2)t^-2)/4

Is the question complete? Before you move on to the next question you can reread the question to see if you have fully answered it.

In this case, we need to finally find the value of dy/dx at t=2. 

To do this the value of t=2 needs to be substituted into the equation for dy/dx that we found. The value retrieved from this is 32.