What is the extreme f(x)=cos(6x) ?

The extreme f(x)=cos(6x) is Maximum(pi/3 n,1),Minimum(pi/6+pi/3 n,-1)

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extreme f(x)=cos(6x)

extreme points

f (x) = cos (6 x)

Maximum (\frac{π}{3} n, 1), Minimum (\frac{π}{6} + \frac{π}{3} n, - 1)

Solution steps

Find the critical points:

x = \frac{π}{3} n, x = \frac{π}{6} + \frac{π}{3} n

Domain of

cos (6 x) : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{π}{3} n < x < \frac{π}{6} + \frac{π}{3} n,

Increasing

: \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Plug the extreme point

x = \frac{π}{3} n

into

cos (6 x) \Rightarrow y = 1

Maximum (\frac{π}{3} n, 1)

Plug the extreme point

x = \frac{π}{6} + \frac{π}{3} n

into

cos (6 x) \Rightarrow y = - 1

Minimum (\frac{π}{6} + \frac{π}{3} n, - 1)

Maximum (\frac{π}{3} n, 1), Minimum (\frac{π}{6} + \frac{π}{3} n, - 1)

f (x) = x^{2} - 6, (- 2, 4)

2 x^{3} + 3 x^{2} + 12 x - 4

B (1 + p)

f (x) = - x^{3} - 9 x^{2} - 15 x + 1

f (x, y) = 4 y^{2} + 5 x^{2} - 9 y + 8 x - 19

What is the extreme f(x)=cos(6x) ?
The extreme f(x)=cos(6x) is Maximum(pi/3 n,1),Minimum(pi/6+pi/3 n,-1)