What is the extreme sin(x)+cos(x) ?

The extreme sin(x)+cos(x) is Maximum(pi/4+2pin,sqrt(2)),Minimum((5pi)/4+2pin,-sqrt(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme sin(x)+cos(x)

extreme points

sin (x) + cos (x)

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

Solution steps

Find the critical points:

x = \frac{π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Domain of

sin (x) + cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{4} + 2 πn,

Decreasing

: \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn,

Increasing

: \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{4} + 2 πn

into

sin (x) + cos (x) \Rightarrow y = 2

Maximum (\frac{π}{4} + 2 πn, 2)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

sin (x) + cos (x) \Rightarrow y = - 2

Minimum (\frac{5 π}{4} + 2 πn, - 2)

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

f (x) = \frac{x + 6}{x - 6}

\frac{x ^{2} + x - 20}{x + 5}

X^{3}

f (x) = (x - 6)^{2} - 9

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

What is the extreme sin(x)+cos(x) ?
The extreme sin(x)+cos(x) is Maximum(pi/4+2pin,sqrt(2)),Minimum((5pi)/4+2pin,-sqrt(2))