What is the extreme f(x)=5sin(3x)-5 ?

The extreme f(x)=5sin(3x)-5 is Maximum(pi/6+(2pi)/3 n,0),Minimum(pi/2+(2pi)/3 n,-10)

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extreme f(x)=5sin(3x)-5

extreme points

f (x) = 5 sin (3 x) - 5

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 0), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 10)

Solution steps

Find the critical points:

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

Domain of

5 sin (3 x) - 5 : - \infty < x < \infty

Find intervals:

Increasing

: \frac{2 π}{3} n \leq x < \frac{π}{6} + \frac{2 π}{3} n,

Decreasing

: \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n,

Increasing

: \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Plug the extreme point

x = \frac{π}{6} + \frac{2 π}{3} n

into

5 sin (3 x) - 5 \Rightarrow y = 0

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 0)

Plug the extreme point

x = \frac{π}{2} + \frac{2 π}{3} n

into

5 sin (3 x) - 5 \Rightarrow y = - 10

Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 10)

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 0), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 10)

\frac{x ^{2} - x - 6}{x ^{2} - 7 x + 10}

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

1 - x^{3}

f (t) = 5 u (t - 2)

G (x, y) = 50000 x + 40000 y - 10 x^{2} - 20 y^{2} - 10 x y

What is the extreme f(x)=5sin(3x)-5 ?
The extreme f(x)=5sin(3x)-5 is Maximum(pi/6+(2pi)/3 n,0),Minimum(pi/2+(2pi)/3 n,-10)