# The X-Value

1.Let f(x)=x^4-5x^3-7x^2+x-6 and g(x)=x^3-12x-5. Plot f(x) and g(x) on the same graph, with f(x) in red and g(x) in blue. Use an appropriate domain and range that show all key features (intercepts, maximums, minimums, intersections) of the two functions. Label the axes appropriately. Use specialized ticks, not the defaults given by Mathematica

2. Use Solve commands to find the location (the x-value is sufficient) of all intersections of f(x) and g(x) in Problem 1.
3.Use Solve commands to find the location of all x-intercepts of each function from Problem 1.
4.For what value(s) of a (if any) is the graph of f(x)=a x-4 tangent to the graph of g(x)=-(2/a) x^2? Work this problem in two ways: 1) use the Manipulate command and a plot to estimate the value(s), 2) algebraically determine the exact value(s).

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