What is the extreme f(x)=-2+5sin(pi/(12)(x-2)) ?

The extreme f(x)=-2+5sin(pi/(12)(x-2)) is Maximum(8+24n,3),Minimum(20+24n,-7)

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extreme f(x)=-2+5sin(pi/(12)(x-2))

extreme points

f (x) = - 2 + 5 sin (\frac{π}{12} (x - 2))

Maximum (8 + 24 n, 3), Minimum (20 + 24 n, - 7)

Solution steps

Find the critical points:

x = 8 + 24 n, x = 20 + 24 n

Domain of

- 2 + 5 sin (\frac{π}{12} (x - 2)) : - \infty < x < \infty

Find intervals:

Increasing

: 24 n \leq x < 8 + 24 n,

Decreasing

: 8 + 24 n < x < 20 + 24 n,

Increasing

: 20 + 24 n < x < 24 + 24 n

Plug the extreme point

x = 8 + 24 n

into

- 2 + 5 sin (\frac{π}{12} (x - 2)) \Rightarrow y = 3

Maximum (8 + 24 n, 3)

Plug the extreme point

x = 20 + 24 n

into

- 2 + 5 sin (\frac{π}{12} (x - 2)) \Rightarrow y = - 7

Minimum (20 + 24 n, - 7)

Maximum (8 + 24 n, 3), Minimum (20 + 24 n, - 7)

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

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

f (x) = - 4 x^{5} ln (2 x)

f (x) = \frac{x ^{3}}{x} - 3 x^{2} - 7 x

y = x^{3} + 3 x^{2} + 3 x + 1

What is the extreme f(x)=-2+5sin(pi/(12)(x-2)) ?
The extreme f(x)=-2+5sin(pi/(12)(x-2)) is Maximum(8+24n,3),Minimum(20+24n,-7)