Parabolas, Trigonometry, Integrals, and Derivatives oh my!

Instructions!
Locate the minimum/maximum, how does changing the parts of the graph change the equation?
Integrate this!
How does the idea of a Riemann Sums contribute to the definition of an integral?
Derivatives
Use the graph, and notice the plot of the f' function in pink. Why is there no equation at certain points on the graph? What is the f' function representing?
Trig
Play with the sliders on the trig graphs above. Explain how the slider changes each type of graph. How does it affect the equation?
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Information: Parabolas, Trigonometry, Integrals, and Derivatives oh my!