Draw the graph of y=1-(x^3)/2
a) Choose a point S1 on the graph at which the tangent at S1 meets the graph again at another point T1 . Use the graph to estimate the coordinates of T1.
b) using differentiation , find the gradients of the graph at S1 and T1.
c) find the ratio of the gradient of the graph at S1 to the gradient of the graph at T1.
d) repeat the steps (a) to (c) , choosing another three point S2 , S3 , S4 .
e) make a conclusion about the ratio of the gradient of the gradient of the graph at any point S to the gradient of the graph at T where T is another point of intersection of the graph and its tangent at S.
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