What is the extreme 2cos(2x) ?

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

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extreme 2cos(2x)

extreme points

2 cos (2 x)

Maximum (πn, 2), Minimum (\frac{π}{2} + πn, - 2)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

2 cos (2 x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn < x < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

2 cos (2 x) \Rightarrow y = 2

Maximum (πn, 2)

Plug the extreme point

x = \frac{π}{2} + πn

into

2 cos (2 x) \Rightarrow y = - 2

Minimum (\frac{π}{2} + πn, - 2)

Maximum (πn, 2), Minimum (\frac{π}{2} + πn, - 2)

0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300

f (x) = \frac{( x ^{4} )}{4} - 2 x^{3} + 1

81 - x^{2}

f (x) = \frac{3 - 4 x}{x ^{2} + 1}, - 2 \leq x \leq 4

y = 4 x + 8 (\frac{20000}{x})

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