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Let f(x) be a twice differentiable function (i.e. its first and second derivatives exist at all...

Let f(x) be a twice differentiable function (i.e. its first and second derivatives exist at all points). (a) What can you say about f(x) when f 0 (x) is positive? How about when f 0 (x) is negative? (b) What can you say about f 0 (x) when f 00(x) is positive? How about when f 00(x) is negative? (c) What can you say about f(x) when f 00(x) is positive? How about when f 00(x) is negative? (d) Let c be a number where f(c) is defined, f 0 (c) = 0, and f 00(c) is positive. What can you tell me about the point (c, f(c)) on the graph?

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