Consider the function f(x) = {2x3 - x2 +3x if x < 2, -36 +31x - 2x2 if x greater than or equal to 2}
a. Explain why f(x) is continuous and differentiable.
b. Graph the function in the xy plane where both x and y are non-negative. Find the positive values of x over which the function is increasing and decreasing.
c. Calculate the derivative of the function and explain why the sign of the derivative makes sense given your answers to part (b).
d. In your graph in (b), what value(s) of x minimize(s) the function for the domain and range given in (b)? Is df/dx=0 for these values of x? Why or why not?
e. Explain why x=2 is a point of inflection for f(x).