What is the extreme cos(t) ?

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

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extreme cos(t)

extreme points

cos (t)

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

Solution steps

Find the critical points:

t = 2 πn, t = π + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn < t < π + 2 πn,

Increasing

: π + 2 πn < t < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

cos (t) \Rightarrow y = 1

Maximum (2 πn, 1)

Plug the extreme point

x = π + 2 πn

into

cos (t) \Rightarrow y = - 1

Minimum (π + 2 πn, - 1)

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

f (x) = x^{4} - 32 x^{2} + 8

f (x, y) = 2 x^{3} - 5 x y^{2} + 4 y^{3}

f (x, y) = 2 x^{2} - x y + y^{2} - 6 x - 9 y + 7

12 x^{\frac{2}{3}} - 8 x

f (x) = 9 - x^{2}, - 3 \leq x \leq 2

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