What is the extreme f(x)=5sin(2x)+3 ?

The extreme f(x)=5sin(2x)+3 is Maximum(pi/4+pin,8),Minimum((3pi)/4+pin,-2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=5sin(2x)+3

extreme

Maximum (\frac{π}{4} + πn, 8), Minimum (\frac{3 π}{4} + πn, - 2)

Solution steps

Find the critical points:

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

Domain of

5 sin (2 x) + 3 : - \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

5 sin (2 x) + 3 \Rightarrow y = 8

Maximum (\frac{π}{4} + πn, 8)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

5 sin (2 x) + 3 \Rightarrow y = - 2

Minimum (\frac{3 π}{4} + πn, - 2)

Maximum (\frac{π}{4} + πn, 8), Minimum (\frac{3 π}{4} + πn, - 2)

What is the extreme f(x)=5sin(2x)+3 ?
The extreme f(x)=5sin(2x)+3 is Maximum(pi/4+pin,8),Minimum((3pi)/4+pin,-2)