What is the extreme cos(x) ?

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

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extreme cos(x)

extreme points

cos (x)

Maximum (2 πn, 1), Minimum (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:

Decreasing

: 2 πn < x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

cos (x) \Rightarrow y = 1

Maximum (2 πn, 1)

Plug the extreme point

x = π + 2 πn

into

cos (x) \Rightarrow y = - 1

Minimum (π + 2 πn, - 1)

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

f (x) = (x - 2)^{2} + 5

f (x) = \frac{x + 1}{2 x + 39 + x}

x^{3} (x + 5)^{2} + 5

ln (tan (x) + sec (x))

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