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Second Derivative of a Function- Exploration

Autor:Sarah Toosarvandani, Kenneth Wright
This applet displays a function f(x), its derivative f '(x) and its second derivative f ''(x). Grab open blue circles to modify the function f(x). Grab a solid circle to move a "test point" along the f(x) graph or along the f '(x) graph.

Instructions

Change the settings so that only the "Test point" and "f(x)" boxes are checked.
Polynomial Degree for f(x)= 3

Move the blue dot so that it is at the point (-9,0). What is the slope?

Move the blue dot so that it is at the point (-7,3). What is the slope?

Move the blue dot so that it is at the point (-5,4.5). What is the slope?

Move the blue dot so that it is at the point (-3,3). What is the slope?

Is the value of f'(x), i.e. the slope of the tangent line, increasing or decreasing, as x moves from left to right over the interval [-9,0]

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Is the graph concave up or concave down over the interval [-9,0]?

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Is the value of f'(x), i.e. the slope of the tangent line, increasing or decreasing, as x moves from left to right over the interval [0,9]?

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Is the graph concave up or concave down over the interval [0,9]?

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In general, when f'(x) is decreasing, the graph of f(x) will be concave down and when f'(x) is increasing, the graph of f(x) will be _________________?

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