What is the extreme y=1250sin(2x) ?

The extreme y=1250sin(2x) is Maximum(pi/4+pin,1250),Minimum((3pi)/4+pin,-1250)

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extreme y=1250sin(2x)

extreme points

y = 1250 sin (2 x)

Maximum (\frac{π}{4} + πn, 1250), Minimum (\frac{3 π}{4} + πn, - 1250)

Solution steps

Find the critical points:

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

Domain of

1250 sin (2 x) : - \infty < x < \infty

Find intervals:

Increasing

: πn \leq x < \frac{π}{4} + πn,

Decreasing

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

Increasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

1250 sin (2 x) \Rightarrow y = 1250

Maximum (\frac{π}{4} + πn, 1250)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

1250 sin (2 x) \Rightarrow y = - 1250

Minimum (\frac{3 π}{4} + πn, - 1250)

Maximum (\frac{π}{4} + πn, 1250), Minimum (\frac{3 π}{4} + πn, - 1250)

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

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

f (x) = - 4 x^{3} + 12 x^{2} - 10

f (x) = 2 x + 7 ln (x)

68 - 11

What is the extreme y=1250sin(2x) ?
The extreme y=1250sin(2x) is Maximum(pi/4+pin,1250),Minimum((3pi)/4+pin,-1250)