What is the extreme f(t)=25cos(2t) ?

The extreme f(t)=25cos(2t) is Maximum(pin,25),Minimum(pi/2+pin,-25)

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extreme f(t)=25cos(2t)

extreme points

f (t) = 25 cos (2 t)

Maximum (πn, 25), Minimum (\frac{π}{2} + πn, - 25)

Solution steps

Find the critical points:

t = πn, t = \frac{π}{2} + πn

Domain of

25 cos (2 t) : - \infty < t < \infty

Find intervals:

Decreasing

: πn < t < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < t < π + πn

Plug the extreme point

x = πn

into

25 cos (2 t) \Rightarrow y = 25

Maximum (πn, 25)

Plug the extreme point

x = \frac{π}{2} + πn

into

25 cos (2 t) \Rightarrow y = - 25

Minimum (\frac{π}{2} + πn, - 25)

Maximum (πn, 25), Minimum (\frac{π}{2} + πn, - 25)

f (x) = - 2 x^{3} + 24 x^{2} - 42 x + 7

f (x) = - 0.01 x^{2} + 120 x + 200000

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

\frac{x}{ln ( x ^{2} )}

x^{2 x}

What is the extreme f(t)=25cos(2t) ?
The extreme f(t)=25cos(2t) is Maximum(pin,25),Minimum(pi/2+pin,-25)