Gradient Function :: Papers

Gradient Function For this investigation, I have to find the relationship between a point of any non-linear graph and the gradient of the tangent, which is the gradient function. First of all, I have to define the word, 'Gradient'. Gradient means the slope of a line or a tangent at any point on a curve. A tangent is basically a line, curve, or surface that touches another curve but does not cross or intersect it. To find a gradient, observe the graph below: [IMAGE][IMAGE] All you have to do to find the gradient is to divide the change in X with the change in Y. In this case, on the graph above, AB and you would have gotten the BC gradient for that particular point of the graph. I am going start by finding the gradient function of y=x ², y=2x ², and then y=ax ². I will move on finding the gradient function of y=x ³, y=2x ³, and finally y=ax ³. I will then find the similarities and generalise y=axà ¢Ã‚ ¿ where 'a' and 'n' are constants, and then investigate the Gradient function for any curves of my choice. I will first find the gradient of tangents on the graph y=x ² by drawing the graph (page 3), and then find the gradient for a number of selected points on the graph: Point X Change in Y Change in X Gradient a -3 6 -1 -6 b -2 4 -1 -4 c -1 2 -1 -2 d 1 2 1 2 e 2 4 1 4 f 3 6 1 6 As you can see, the gradient is always twice the value of its original X value Where y=x ². So the gradient function has to be f `(x)=2x for