# Thread: Slope of secant line or curve

1. ## Slope of secant line or curve

Please find the slope of the secant line or the following curve in terms of x and h.
1. f(x) = 2x - 4
2. f(x) = x^2 - 2x

Can someone help solve these problems. What is h in these problems?

Thank you

2. Originally Posted by oceanmd
Please find the slope of the secant line or the following curve in terms of x and h.
1. f(x) = 2x - 4
2. f(x) = x^2 - 2x

Can someone help solve these problems. What is h in these problems?

Thank you

Originally Posted by Mr Fantastic
They probably want you to find the gradient of the line segment that joins the point (x, f(x)) and the point (x+h, f(x+h)).
When I said new question, new thread, I didn't mean that you double post the question by starting a new thread. It was advice to remember for next time.

3. ## slope of the secant line

I was hoping somebody else would answer. What exactly do I need to do here? Do I need to find the average rate of change? I guess I need to understand what is the slope of the secant line of f(x) = 2x-4. The slope of the line is 2.

Will someone please explain how to do this kind of problems.

Thank you

4. Originally Posted by oceanmd
I was hoping somebody else would answer.

Mr F says: Then what you do is you say that you still don't quite understand what to do - at the original thread. I will point out that this sort of comment could be be considered by some as insulting ....

What exactly do I need to do here? Do I need to find the average rate of change?

Mr F says: I told you what to do. What part of what I said do you not understand?

I guess I need to understand what is the slope of the secant line of f(x) = 2x-4. The slope of the line is 2.

Mr F says: The secant is the line joingng the two points. The gradient of a line joining two points that lie on a line will obviously be the gradient of that line that the points lie on. The gradient of the secant joingin any two points on f(x) = 2x - 4 is obviously 2.

Will someone please explain how to do this kind of problems.

Mr F says: If you were clearer in saying what exactly you still don't understand it would be easier to help you.

Thank you
For f(x) = x^2 - 2x:

You have the points A(x, x^2 - 2x) and the B(x+h, (x+h)^2 - 2(x+h)). The gradient of the secant is the gradient of the line joining those two points. That's what the question wants you to do (at least that what it looks like it wants you to do - you obviously have not included all of the question since h is not defined).

Do you know how to calculate the gradient of the line joining two points?

5. ## slope of the secant line

After I simplified, the result I got is 2x+h-2. Does it mean that slope of the secant line is 2. Thank you in advance.

6. Originally Posted by oceanmd
After I simplified, the result I got is 2x+h-2. Does it mean that slope of the secant line is 2. Thank you in advance.
No. The gradient of the secant is 2x + h - 2.

It means that in the limit of h --> 0, the gradient of the tangent at any point on the curve is 2x - 2.

7. This is really helpful Thanks Mr F