What is the extreme cos(2x) ?

The extreme cos(2x) is Maximum(pin,1),Minimum(pi/2+pin,-1)

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extreme cos(2x)

extreme points

cos (2 x)

Maximum (πn, 1), Minimum (\frac{π}{2} + πn, - 1)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

cos (2 x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn < x < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

cos (2 x) \Rightarrow y = 1

Maximum (πn, 1)

Plug the extreme point

x = \frac{π}{2} + πn

into

cos (2 x) \Rightarrow y = - 1

Minimum (\frac{π}{2} + πn, - 1)

Maximum (πn, 1), Minimum (\frac{π}{2} + πn, - 1)

f (x) = - 6 x^{2} - 9 x y - 7 y^{2} - 99 x - 96 y + 5

f (x) = lo g_{e} (x)

P (x, y) = x + y^{2} - 10 x^{2} y^{2} + 9 y^{6}

f (x) = - x^{\frac{2}{3}} (x - 1), - 1 \leq x \leq 1

f (x) = t 25 - t^{2}

What is the extreme cos(2x) ?
The extreme cos(2x) is Maximum(pin,1),Minimum(pi/2+pin,-1)