Question

At the point (0,3) find the rate of change in the slope of the curve with respect to x.

Answer 1

\[\frac{ dy }{ dx }=\frac{ y-2x }{ 2y-x }\]

Answer 2

So I got 1/2 when I plugged that point into the derivative, but my teacher did something else once they got the 1/2...

Answer 3

What did your teacher do?

Answer 4

@Ivitt

Answer 5

If your teacher did that, it's best to follow that instruction. It might be the most accurate, more accurate than mine. :)

Answer 6

Yeah but I need an explanation as to why they did what they did

Answer 7

Hey girl :)
Notice the question is asking for the rate change of the slope.
So we need to find the derivative of this derivative function.

By plugging in (0,3) you determined that y'=1/2.
Good, you'll need these three pieces of information after you find your derivative of your derivative.

Answer 8

Rate of change in the slope... means the derivative of the slope.

You don't just plug in numbers, you find the derivative of what you're given, first. THEN plug in numbers.

Answer 9

x=0
y=3
y'=1/2

You apply quotient rule and then just plug those three things in.

Answer 10

Oh so before I plug in the point to the derivative, I take the derivative of the derivative, correct?

Answer 11

Correct.

Answer 12

Once you plug a value in for the variable,
you are no longer allowing it to vary or change.

So when you measure rate of change,
you must allow the thing to change before pinning it down to a location.

That was not a very articulate way to phrase that :P
Whatever though...

Answer 13

Lol no I understand what you're saying! :P Thank you very much!!