How can I determine a value of gradient from a graph if the line is curved. (not a straight line)

This is where Calculus comes in

If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw at a particular point on that curve.

You can do it graphically by drawing the tangent line, but this is not very accurate. If you need to be as accurately as possible, you should read-off many points from the graph in the neighborhood of the point where you want to measure the gradient.

You then fit a polynomial function through the points. You must take the number of points to be much larger than the degree of the polynomial fit function. Then you extract the derivative from the results of the fit.

To determine the value of the gradient from a curved graph, you can use calculus. By finding the derivative of the function that represents the curve, you can calculate the slope of the tangent line at any point on the curve.

Here's a step-by-step process to determine the value of the gradient from a curved graph:

1. Identify the function that represents the curve. This function will help you find the derivative.

2. Apply the rules of differentiation to find the derivative of the function. This involves taking the derivative of each term in the function and simplifying the result.

3. Once you have the derivative, substitute the x-coordinate of the point on the curve for which you want to find the gradient. This will give you the slope of the tangent line at that point.

It's important to note that finding the derivative algebraically can be challenging for complex functions. In such cases, you can use numerical methods or software to approximate the derivative.

By following this process, you can determine the value of the gradient (slope) from a curved graph using calculus.