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Derivative sketcher quadratic

In this diagram, the red dot shows the value of the instantaneous rate of change of the curve at the blue point. Move the blue point, to see the pattern of the instantaneous slopes for the curve.

Question 1

What shape do the values of the slopes create?

Question 2

The equation for the curve is given by find f'(x).

Question 3

If I were to graph the answer to question 2, what would be the relation between the graph of question 2, and the shape created by the red slope values?