The derivative of a polynomial function, f(x), is represented by the equation f '(x) = -2x(x-3)^2 . Additionally, f(1) = -3 and the graph of f(x) is concave up at x = 1. Use this information to answer the following questions.

a) At what value(s) of x does the graph of f(x) have a relative maximum? A relative minimum? Justify your reasoning.

b) On what interval(s) is the graph of f(x) increasing? Decreasing? Justify your reasoning.

c) What is the tangent line approximation of f(1.1)? Is this estimate greater or less than the actual value of f(1.1)? Give a reason for your answer.