Question 1 Given f, f', and f" below (a) (b) 10(1-x) 10(1+2z) f(x)=(5-2x), f'(x) = f(x) 3x1/3 9x4/3 X x²+9 f(x) f'(x) f" (z) x² 9' (x² - 9)2' 2r(x²+27) (x-9)3 Sketch the curve of f by.... ⚫finding its domain. ⚫ finding the x- and y-intercepts, if any. ⚫ finding the equations of the horizontal and vertical asymptotes, if any. ⚫finding the interval of monotonicity. ⚫finding the intervals of concavity. ⚫ finding the inflection points, if any. Label any intercepts, asymptotes, and inflection points. Question 2 Consider the functions and their derivatives from Question 1, both (a) and (b). (a) Use the first derivative test to find the local extrema (if any). (b) Use the second derivative test to find the local extrema (if any). (c) Only for f(x) = (5 - 2x) x ³. Does one test seem to perform better than the other? Feel free to use your work from Question 1. Question 3 axb Find constants a and b in the function f(x): local minimum at x = In(x) such that f(): =1 and the function has a 2

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