Introducing Derivatives - The Slope Function

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Move point A along the function graph and make a conjecture about the shape of the path of point S, which corresponds to the slope function.
Turn on the trace of point S. Move point A to check your conjecture. Hint: Right-click point S (MacOS: Ctrl-click, tablet: long tap) and select Trace on.
Find the equation of the resulting slope function and enter it into the Input Bar using g(x)=... Move point A along the graph of function f. If your prediction is correct, the trace of point S will match the graph of your function g.
Change the equation of the initial polynomial f to produce a new problem. For example, enter f(x)= 2 x² into the Input Bar. Hint: You might want to zoom if point A lays outside of the visible area after changing the function.

1.		Enter the polynomial f(x) = x^2/2 + 1.
2.		Create a new point A on function f. Hint: Point A can only be moved along the function.
3.		Create tangent a to function f through point A.
4.		Create the slope of tangent a using m = Slope(a).
5.		Define point S: S = (x(A), m). Hint: `x(A)` gives you the x-coordinate of point A.
6.		Connect points A and S using a segment.
7.		Turn on the trace of point S. Hint: Right-click point S (MacOS: Ctrl-click, tablet: long click) and select Trace on.