G'day,
I'm having a problem with the following question I'm doing in a Calculus exercise. Is anybody able to help me out solving it. And also if possible could you show working so I can understand whats going on.

"
In the case below, the equation of a curve is given, and two points P & Q on the curve are defined. Write down the gradient of the chord PQ.
Curve: y=12/x
Point P: x = 3
Point Q: x = (3+h)
"

Thanks,

Matthew

Is anybody able to help me out solving it. And also if possible could you show working so I can understand whats going on.


Which one do you want? Do you want help solving it, or do you want someone to solve it for you? I'll do the former, but not the latter.


"
In the case below, the equation of a curve is given, and two points P & Q on the curve are defined. Write down the gradient of the chord PQ.
Curve: y=12/x
Point P: x = 3
Point Q: x = (3+h)
"


The gradient is simply the slope of the chord. You have two points, to that you must apply the formula for the slope. There is no calculus involved.

Isn't gradF on a single variable expression just the derivative?

What I need is to find out the 'y' ordinates for the 2 points (P & Q). And then also work out the Gradient from this.
I've been trying to work it out, but keep getting the wrong answer. So I am thinking that I'm making the mistake, somewhere in my algebra working.

I get ..... -4 / [3+h]

The gradient is simply the slope of the chord. You have two points, to that you must apply the formula for the slope. There is no calculus involved.I guess it is part of an introduction to calculus... as h tends to zero you get the differential of the point on the slope at x=3, y=4, which is -4/3 (I think).

Anyhoo - You have the X/Y co-ordinates at point x=3 (hint: use y=12/x).
You can also use the same hint to work out the co-ordinates at point x=(3+h).

Then calculate the gradient: (change in Y / change in X) for the slope between the two points, one of which will be (3,4), the other will be expressed in terms of "h".