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# (Solved): 1) Find the absolute maximum an absolute minimum value of $$f(x)=x^{3}-6 x^{2}+9 x+2$$ on $$[-1 ... 1) Find the absolute maximum an absolute minimum value of \( f(x)=x^{3}-6 x^{2}+9 x+2$$ on $$[-1,4]$$. You must show all your work. 15 points 2) Consider the function $$f(x)=2 \sqrt{x}-x$$. Find the following: 25 points. You must show all derivative/algebra. a) The Domain b) All intercepts c) Determine if $$f(x)$$ is odd, even, and/or periodic d) All asymptotes e) All intervals of increase or decreasing f) All local maximums and minimums g) Concavity and inflection points h) Make a sketch of the graph 3) Evaluate $$\lim _{x \rightarrow \infty} \frac{(\ln x)^{2}}{x} \quad 15$$ points You must show all your work. 4) A rectangular storage container with an open top is to have a volume of 10 $$\mathrm{m}^{3}$$. The length of this base is twice the width. Material for the base costs $$\ 10$$ per square meter. Material for the side's costs $$\ 6$$ per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.) 20 pints $$\quad$$ You must show all your work.

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