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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.

Find the absolute maximum and absol