What is the extreme cos(2x+5) ?

The extreme cos(2x+5) is Maximum((-5+2pi)/2+pin,1),Minimum((3pi-5)/2+pin,-1)

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extreme cos(2x+5)

extreme points

cos (2 x + 5)

Maximum (\frac{- 5 + 2 π}{2} + πn, 1), Minimum (\frac{3 π - 5}{2} + πn, - 1)

Solution steps

Find the critical points:

x = \frac{- 5 + 2 π}{2} + πn, x = \frac{3 π - 5}{2} + πn

Domain of

cos (2 x + 5) : - \infty < x < \infty

Find intervals:

Increasing

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

Decreasing

: \frac{- 5 + 2 π}{2} + πn < x < \frac{3 π - 5}{2} + πn,

Increasing

: \frac{3 π - 5}{2} + πn < x < π + πn

Plug the extreme point

x = \frac{- 5 + 2 π}{2} + πn

into

cos (2 x + 5) \Rightarrow y = 1

Maximum (\frac{- 5 + 2 π}{2} + πn, 1)

Plug the extreme point

x = \frac{3 π - 5}{2} + πn

into

cos (2 x + 5) \Rightarrow y = - 1

Minimum (\frac{3 π - 5}{2} + πn, - 1)

Maximum (\frac{- 5 + 2 π}{2} + πn, 1), Minimum (\frac{3 π - 5}{2} + πn, - 1)

f (x) = 2 (x + 3)^{2} - 18

x^{2} + x + 3

x^{2} - 9

y = - \frac{3}{4 x}

\frac{1}{x ^{2} - x - 6}

What is the extreme cos(2x+5) ?
The extreme cos(2x+5) is Maximum((-5+2pi)/2+pin,1),Minimum((3pi-5)/2+pin,-1)