What is the extreme f(x)=sin(10x) ?

The extreme f(x)=sin(10x) is Maximum(pi/(20)+pi/5 n,1),Minimum((3pi)/(20)+pi/5 n,-1)

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extreme f(x)=sin(10x)

extreme points

f (x) = sin (10 x)

Maximum (\frac{π}{20} + \frac{π}{5} n, 1), Minimum (\frac{3 π}{20} + \frac{π}{5} n, - 1)

Solution steps

Find the critical points:

x = \frac{π}{20} + \frac{π}{5} n, x = \frac{3 π}{20} + \frac{π}{5} n

Domain of

sin (10 x) : - \infty < x < \infty

Find intervals:

Increasing

: \frac{π}{5} n \leq x < \frac{π}{20} + \frac{π}{5} n,

Decreasing

: \frac{π}{20} + \frac{π}{5} n < x < \frac{3 π}{20} + \frac{π}{5} n,

Increasing

: \frac{3 π}{20} + \frac{π}{5} n < x < \frac{π}{5} + \frac{π}{5} n

Plug the extreme point

x = \frac{π}{20} + \frac{π}{5} n

into

sin (10 x) \Rightarrow y = 1

Maximum (\frac{π}{20} + \frac{π}{5} n, 1)

Plug the extreme point

x = \frac{3 π}{20} + \frac{π}{5} n

into

sin (10 x) \Rightarrow y = - 1

Minimum (\frac{3 π}{20} + \frac{π}{5} n, - 1)

Maximum (\frac{π}{20} + \frac{π}{5} n, 1), Minimum (\frac{3 π}{20} + \frac{π}{5} n, - 1)

f (x) = \frac{1}{8}

f (x) = x^{5} + x^{4}

f (x) = x^{3} - 6 x^{2} + 7

m = - 5, (3, 9)

\frac{x - 1}{( x + 3 ) ( x - 2 )}

What is the extreme f(x)=sin(10x) ?
The extreme f(x)=sin(10x) is Maximum(pi/(20)+pi/5 n,1),Minimum((3pi)/(20)+pi/5 n,-1)