What is the extreme f(x)=5*sin(x-(5pi)/6) ?

The extreme f(x)=5*sin(x-(5pi)/6) is Minimum(pi/3+2pin,-5),Maximum((4pi)/3+2pin,5)

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extreme f(x)=5*sin(x-(5pi)/6)

extreme points

f (x) = 5 \cdot sin (x - \frac{5 π}{6})

Minimum (\frac{π}{3} + 2 πn, - 5), Maximum (\frac{4 π}{3} + 2 πn, 5)

Solution steps

Find the critical points:

x = \frac{π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Domain of

5 \cdot sin (x - \frac{5 π}{6}) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{3} + 2 πn,

Increasing

: \frac{π}{3} + 2 πn < x < \frac{4 π}{3} + 2 πn,

Decreasing

: \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{3} + 2 πn

into

5 \cdot sin (x - \frac{5 π}{6}) \Rightarrow y = - 5

Minimum (\frac{π}{3} + 2 πn, - 5)

Plug the extreme point

x = \frac{4 π}{3} + 2 πn

into

5 \cdot sin (x - \frac{5 π}{6}) \Rightarrow y = 5

Maximum (\frac{4 π}{3} + 2 πn, 5)

Minimum (\frac{π}{3} + 2 πn, - 5), Maximum (\frac{4 π}{3} + 2 πn, 5)

- x^{2} - 2 x + 1

f (x) = e^{x} + 2

\frac{5}{x + 2}

f (x) = 3^{x} + 1

x x - 1

What is the extreme f(x)=5*sin(x-(5pi)/6) ?
The extreme f(x)=5*sin(x-(5pi)/6) is Minimum(pi/3+2pin,-5),Maximum((4pi)/3+2pin,5)