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Investigating the slope of y=x^2

Move the point A (purple) along the curve for y=x^2 and observe what happens to the tangent line (red). Can you find a connection between the co-ordinate of the point A and the slope of the tangent line? (Hint: Make a table of some values to try and spot the pattern.)
Now change the function to y=x^3 and repeat the experiment.