What is the extreme 6cos^2(x)-12sin(x) ?

The extreme 6cos^2(x)-12sin(x) is Minimum(pi/2+2pin,-12),Maximum((3pi)/2+2pin,12)

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extreme 6cos^2(x)-12sin(x)

extreme points

6 cos^{2} (x) - 12 sin (x)

Minimum (\frac{π}{2} + 2 πn, - 12), Maximum (\frac{3 π}{2} + 2 πn, 12)

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Domain of

6 cos^{2} (x) - 12 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn,

Decreasing

: \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

6 cos^{2} (x) - 12 sin (x) \Rightarrow y = - 12

Minimum (\frac{π}{2} + 2 πn, - 12)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

6 cos^{2} (x) - 12 sin (x) \Rightarrow y = 12

Maximum (\frac{3 π}{2} + 2 πn, 12)

Minimum (\frac{π}{2} + 2 πn, - 12), Maximum (\frac{3 π}{2} + 2 πn, 12)

f (x) = 6 x + \frac{8}{x}

x^{\frac{3}{5}}

+ \frac{1}{4 x - 8}

f (x) = \frac{8.7 x + 0.2}{x ^{2} - 4.5 x + 7.5}

f (t) = \frac{e ^{t}}{t ^{2} + 1}, (0, 3)

What is the extreme 6cos^2(x)-12sin(x) ?
The extreme 6cos^2(x)-12sin(x) is Minimum(pi/2+2pin,-12),Maximum((3pi)/2+2pin,12)