Let f(x) = x^3 (9x^2)/2 + 6x + 4 Note: On this problem you must use calculus

to find your answer to receive credit! Justify all your answers.

(a) On what interval(s) is f(x) increasing?

(b) On what interval(s) is f(x) concave down?

(c) Where are the local minimums and maximums of f(x)? Make sure you label

each relevant point as a local min, max or neither and backup your answer

with calculus.

(d) What is the value of the absolute minimum and the absolute maximum of

f(x) on the interval [0, 5]?