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(a) Explain how to know when a function decreases at an increasing rate. Use the first...

(a) Explain how to know when a function decreases at an increasing rate. Use the first and second derivative language when you respond.

(b) What is the sign (positive or negative) of the second derivative at the relative minimum of a function? What about a relative maximum? (Assume that the second derivative exists at these extrema). Justify your answers. (Hint: Use concavity in your response).

(c) To optimize a function using calculus requires that you find the derivative of the function to be optimized. To find critical values, what are the two things you need to consider once you've found the first derivative?

(d) Maximum and minimum values of a function can be at points where the graph is smooth or at corners/cusps. What is it about the first derivative that distinguishes between the two?

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