What is the extreme 4cos(x) ?

The extreme 4cos(x) is Maximum(2pin,4),Minimum(pi+2pin,-4)

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extreme 4cos(x)

extreme points

4 cos (x)

Maximum (2 πn, 4), Minimum (π + 2 πn, - 4)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

4 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

4 cos (x) \Rightarrow y = 4

Maximum (2 πn, 4)

Plug the extreme point

x = π + 2 πn

into

4 cos (x) \Rightarrow y = - 4

Minimum (π + 2 πn, - 4)

Maximum (2 πn, 4), Minimum (π + 2 πn, - 4)

f (x) = 2 x^{3} + 3 x^{2} - 36 x - 5

f (x) = (x + 4)^{\frac{2}{3}}

f (x) = - 2 x + 5 ln (2 x)

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

f (x) = 2 cos^{2} (x), 0 \leq x \leq π

What is the extreme 4cos(x) ?
The extreme 4cos(x) is Maximum(2pin,4),Minimum(pi+2pin,-4)