What is the extreme sin(t)-(cos(t)+sin(t)) ?

The extreme sin(t)-(cos(t)+sin(t)) is Minimum(2pin,-1),Maximum(pi+2pin,1)

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extreme sin(t)-(cos(t)+sin(t))

extreme points

sin (t) - (cos (t) + sin (t))

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

Solution steps

Find the critical points:

t = 2 πn, t = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn < t < π + 2 πn,

Decreasing

: π + 2 πn < t < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

sin (t) - (cos (t) + sin (t)) \Rightarrow y = - 1

Minimum (2 πn, - 1)

Plug the extreme point

x = π + 2 πn

into

sin (t) - (cos (t) + sin (t)) \Rightarrow y = 1

Maximum (π + 2 πn, 1)

Minimum (2 πn, - 1), Maximum (π + 2 πn, 1)

f (x) = 3 arctan (2 x)

f (x) = \frac{x + 4}{x + 6}

tan (x) sin (x) + sec (x) cos (2) (x)

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

x - 3 y + 3

What is the extreme sin(t)-(cos(t)+sin(t)) ?
The extreme sin(t)-(cos(t)+sin(t)) is Minimum(2pin,-1),Maximum(pi+2pin,1)