Free response AP Calculus problem..regarding trig.. Soo confused :( Help would be muchly appreciated!!!!?

Question

Given the function f defined by f(x) = cosx -cos^2 x for [-pi,pi]

a) find the x intercepts
b) find the x and y coordinates of all relative max. points of f & justify your answer
c) find the intervals on which the graph is increasing

Answer 1

f(x) = cosx -cos^2 x
f(x) = cosx(1-cosx)
cos x = 0 --> x = - pi/2 or pi/2 <-- x -intercepts
1-cosx=0 --> x = 0 <-- x intercepts

Take derivative of f(x) and set it to zero. solve for x.you will get two local max points.

Evalute derivative. When it is positive, f(x) is increasing: when it is negative f(x) is decreasing.

You can do this!!

Answer 2

a) find the x intercept
f(x)= (cosx)(1-cosx)
0=(cosx)(1-cosx)
cosx=0 cosx=1
-pi/2,pi/2 -pi,0,pi
x= -pi, -pi/2, 0, pi/2, pi
b)
take the deriv of this and solve for x at zero to find relative max and min
0= -sinx-2sinxcosx
0= (-1)(sinx)(1+cosx)
zero when
sinx=0 1+cosx=0
cosx= -1
-pi,0,pi -pi/2,pi/2
relative max and min at
-pi, -pi/2, 0, pi/2, pi
c.
when f'(x) is positive it is increasing, when negative decreasing
graph this function on your cal to find out when it is neg and pos

Answer 3

My instructor spent all our evaluation time on quantity and different issues that weren't even interior the unfastened reaction area. i grow to be very suprised by applying the unfastened reaction selections and am unsure how properly i did. i've got faith college board sucker punched me.