What is the extreme f(x)=cos(7x) ?

The extreme f(x)=cos(7x) is Maximum((2pi)/7 n,1),Minimum(pi/7+(2pi)/7 n,-1)

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extreme f(x)=cos(7x)

extreme points

f (x) = cos (7 x)

Maximum (\frac{2 π}{7} n, 1), Minimum (\frac{π}{7} + \frac{2 π}{7} n, - 1)

Solution steps

Find the critical points:

x = \frac{2 π}{7} n, x = \frac{π}{7} + \frac{2 π}{7} n

Domain of

cos (7 x) : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{2 π}{7} n < x < \frac{π}{7} + \frac{2 π}{7} n,

Increasing

: \frac{π}{7} + \frac{2 π}{7} n < x < \frac{2 π}{7} + \frac{2 π}{7} n

Plug the extreme point

x = \frac{2 π}{7} n

into

cos (7 x) \Rightarrow y = 1

Maximum (\frac{2 π}{7} n, 1)

Plug the extreme point

x = \frac{π}{7} + \frac{2 π}{7} n

into

cos (7 x) \Rightarrow y = - 1

Minimum (\frac{π}{7} + \frac{2 π}{7} n, - 1)

Maximum (\frac{2 π}{7} n, 1), Minimum (\frac{π}{7} + \frac{2 π}{7} n, - 1)

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

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

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

f (x) = 12 + 2 x - x^{2}, 0 \leq x \leq 5

f (x) = 4 x + y

What is the extreme f(x)=cos(7x) ?
The extreme f(x)=cos(7x) is Maximum((2pi)/7 n,1),Minimum(pi/7+(2pi)/7 n,-1)