Question #2 ( a) Given the sketch of the following function segment, what are the signs of the first and second derivatives? The first derivative is The second derivative is b) Now sketch a function segment that has negative first derivative and positive second derivative. c) If for a given function at point x=a, the first derivative is f'(a) = 0 and the second derivative is f"(a) =1, then what term from class (e.g. intercept, asymptote, local or global maximum, inflection point,etc) best describes this point on the function graph: Answer: d) For another function, a student correctly finds a critical point at x=3 and then correctly calculates that f"(3)=0. The student concludes that x=3 is not a local extremum. Do you agree or disagree with the student's conclusion? Justify with a brief explanation.

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