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

The extreme f(x)=5cos(x)-5sin(x) is Minimum((3pi)/4+2pin,-5sqrt(2)),Maximum((7pi)/4+2pin,5sqrt(2))

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

extreme points

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

Minimum (\frac{3 π}{4} + 2 πn, - 52), Maximum (\frac{7 π}{4} + 2 πn, 52)

Solution steps

Find the critical points:

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn \leq x < \frac{3 π}{4} + 2 πn,

Increasing

: \frac{3 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn,

Decreasing

: \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{3 π}{4} + 2 πn

into

5 cos (x) - 5 sin (x) \Rightarrow y = - 52

Minimum (\frac{3 π}{4} + 2 πn, - 52)

Plug the extreme point

x = \frac{7 π}{4} + 2 πn

into

5 cos (x) - 5 sin (x) \Rightarrow y = 52

Maximum (\frac{7 π}{4} + 2 πn, 52)

Minimum (\frac{3 π}{4} + 2 πn, - 52), Maximum (\frac{7 π}{4} + 2 πn, 52)

\frac{2 x - 4}{3 x + 2}

f (x) = 4 x - 6 x, x > 0

f (x) = x (x + 11) (x - 6)

tan (2 x - 5)

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

What is the extreme f(x)=5cos(x)-5sin(x) ?
The extreme f(x)=5cos(x)-5sin(x) is Minimum((3pi)/4+2pin,-5sqrt(2)),Maximum((7pi)/4+2pin,5sqrt(2))