How to find slope at a point "X" on the given curve.

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Hello All,

How to find a slope at any point on the curve?

I have a curve which is almost negative exponential curve. I have to take a point on the turning point of the curve and then find a slope at that point of the curve. From that point I have to take a tangent line. How I can do that?
 

What defines the "curve"? An anylytical function? An empirical measurement?
 
Re: How to find slope at a point "X" on the given curve.



Please see the above image

- - - Updated - - -

We have points A, B , C etc.
 

You're not exactly answering my question.

I assume the drawing means that the curve is given by points A to G. So strictly speaking, the "curve" is only your imagination. In this case you need to interpolate the curve with a suitable differentiable function to calculate the slope. Or use the slope of the line connecting points C D as a first order approach.
 

hi ravi,
IF the plot is on scaled paper, a measuring rule place on the paper plot would have to be just touching the plotted point and the intersection of the rule with the X and Y coordinates would give you a value from which you could calc' the approx slope.

Again if you know the scaled values, you could try the straight line equation y= mx+C.

E
 

Assuming you want a precise slope for ANY value of X, I find the easiest way is Excel.
It only takes me a few minutes with data entry, plot, curve fit with polynomial & display equation, create product terms of derivative of Y(x)
Enter new x, display dy/dt = slope.
 

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