What is the extreme-cos(x) ?

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

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extreme-cos(x)

extreme points

- cos (x)

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

- cos (x) \Rightarrow y = - 1

Minimum (2 πn, - 1)

Plug the extreme point

x = π + 2 πn

into

- cos (x) \Rightarrow y = 1

Maximum (π + 2 πn, 1)

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

f (x) = 3 e^{x} - e^{3 x}

f (x, y) = x^{3} + 6 x y + 2 y^{2} + 6 x

f (x, y) = 5 x^{2} + 3 x y + y^{2}

f (x, y) = x + y - x y

\frac{- 3 x + 48}{( x - 120 ) ^{9}}

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