Find the value(s) of x for the following. (Enter your answers as a comma-separat

Question

Find the value(s) of x for the following. (Enter your answers as a comma-separated list.)

f(x) = 2 sin2x - 2 cos x,

and

(a)

f(x)

has a local maximum or local minimum.

(b)

f(x)

has a global maximum or global minimum.

3

4

local maximum      x = local minimum      x = Find the value(s) of x for the following. (Enter your answers as a comma-separated list.) f(x) = 2 sin^2x - 2 cos x, and 0 pi (a) f(x) has a local maximum or local minimum. local maximum x = local minimum x = (b) f(x) has a global maximum or global minimum. global maximum x = 3 global minimum x = 4 Leq leq X

Explanation / Answer

f(x) can be written as 2(1-cosx*cosx) - 2cosx

let cosx = y then f(x) = 2-2y-2y^2 = 2 ( 1 - y- y^2)

Then F( x) will have maximum value at y = -1/2

means cosx = -1/2

x = pi/3 and 2*pi/3 it will have maximum value

So it will have maximum value at x = pi/3 and 2pi/3

and minimum value at x = 0 and pi

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