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!