Question

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation y=3x^2 -7x At what rate is y changing when x=8 and is changing at a rate of 3 units/sec?
2 hours ago - 4 days left to answer.
Additional Details
a.
144 units/sec
b.
41 units/sec
c.
51 units/sec
d.
123 units/sec
e.
27 units/sec

Answer 1

-4 days left to answer? that's new...

Answer 2

So all you're doing here is differentiating with respect to t instead of x as normal. Think as though you're doing implicit differentiation!

I'll go ahead and show you:

\[\frac{ d }{ dt } (y)=\frac{ d }{ dt } (3x^2-7x)\]
\[\frac{ dy }{ dt } =6x\frac{ dx }{ dt }-7\frac{ dx }{ dt } \]
Now you're given dx/dt and x, just solve for dy/dt like the problem asks for algebraically! Problem solved.