What is the extreme 5cos(x) ?

The extreme 5cos(x) is Maximum(2pin,5),Minimum(pi+2pin,-5)

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extreme 5cos(x)

extreme points

5 cos (x)

Maximum (2 πn, 5), Minimum (π + 2 πn, - 5)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

5 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

5 cos (x) \Rightarrow y = 5

Maximum (2 πn, 5)

Plug the extreme point

x = π + 2 πn

into

5 cos (x) \Rightarrow y = - 5

Minimum (π + 2 πn, - 5)

Maximum (2 πn, 5), Minimum (π + 2 πn, - 5)

f (x) = \frac{3}{5} (x^{2} - 1)^{\frac{2}{3}}

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

f (x) = \frac{5 e ^{4 x}}{5 x - 3}

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

What is the extreme 5cos(x) ?
The extreme 5cos(x) is Maximum(2pin,5),Minimum(pi+2pin,-5)