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Option 1

Analyze and sketch the graph of the function below. Show all of your work for each section on lined paper. Note: the first option's second derivative has been given to you. Option 1: $f(x)=x_{3}x_{2}?4?andf_{??}(x)=x_{5}2x_{2}?48?$ Option 2: $f(x)=xe_{2x}$ For the function you choose, provide: - the intercepts (both $x$ and $y$ ) - domain and range - eq'ns and types of all asymptotes - the first derivative (factored and simplified fully) - coordinates of all critical points, classified as local max, min or neither - coordinates of any points of inflection - intervals of increase and decrease, stated using set notation - intervals of concavity, stated using set notation All work must be neatly presented on lined paper, clearly showing all your work. Once your analysis is complete, replicate the chart below and record your final answers. Then, using information from your analysis, make a neat sketch of the function on graph paper, by hand (no technology), labelling all key information. Leave all final answers in simplified, exact form.

Given- f(x)=x2?4x3andf?(x)=2x2?48x5(1) For y-intercept x=0?f(0)

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