The function f is such that f(x) = 2 sin^2x - 3 cos^2x for 0

Question

The function f is such that f(x) = 2 sin^2x - 3 cos^2x for 0 <= x <= p.
(i) Express f(x) in the form a + b cos^2x, stating the values of a and b. 
(ii) State the greatest and least values of f(x). 
(iii) Solve the equation f(x) + 1 = 0.

lxelle · Answer

I have found i) a=2, b=-5.

dumbcow · Answer

for part 2) set derivative equal to 0

f(x) = 2 - 5cos^2

f'(x) = -10cos x (-sinx) = 10 sin cos = 0
split up factors
sin x = 0  ----> x = 0,pi
cos x =0 ---> x = pi/2

f(0) = 2-5 = -3
f(pi/2) = 2 - 0 = 2

max = 2,   min = -3

dumbcow · Answer

part 3)

f(x) +1 = 0
3 - 5cos^2 = 0
cos^2 x = 3/5
cos x = +- sqrt(3/5)

take inverse cos
you should get 4 solutions

lxelle · Answer

Is there other simpler way to get ii) answer. I dont get why must it be differentiated.

dumbcow · Answer

haha yes i guess there is because its a trig function
cos^2 is bounded from 0 to 1

just plug in these values for cos^2 to get max,min values

lxelle · Answer

what's the graph for cos^2x

dumbcow · Answer

http://www.wolframalpha.com/input/?i=plot+cos%5E2+x+for+x%3D0+to+2pi

lxelle · Answer

thankssss.