local Extrema, Absolute Extrema, antiderivatives

1)State the intervals on which f(x)=cos(x) - sin(x) is increasing and decreasing on the interval [-∏ , ∏] , and name all the local extrema.

(i don't know where to start on this problem.)

ANSWER: Increasing on [-∏ , -∏/4) and (3∏/4]; decreasing on (-∏/4 , 3∏/4).

Rel max (-∏/4 , √2) Rel min (3∏/4 , -√2).

2) Find the absolute extrema of f(x)=sin(x) - cos(x) on the interval [0,∏]

f'(x)=-cos(x) + sin(x)

g(0)=0

g(∏)=1

This is where i'm stuck.

ANSWER: Abs max √2 at x=3∏/4

3) Use the given information to find f. f'(x)= 3x² -x + 4 f(1)=2

f(x)= x³ -½x² + 4x + c

1 + -½ + 4 + c and f(1) = 2

This is where i stopped. How did my professor get f(x) = x³ -½x² + 4x __-5/2__ ??

ANSWER: f(x) = x³ -½x² + 4x - ⁵⁄₂

Need Help! Thanks everyone!