What is the extreme f(x)=-5cos(3x)-2 ?

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

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extreme f(x)=-5cos(3x)-2

extreme

Minimum (\frac{2 π}{3} n, - 7), Maximum (\frac{π}{3} + \frac{2 π}{3} n, 3)

Solution steps

Find the critical points:

x = \frac{2 π}{3} n, x = \frac{π}{3} + \frac{2 π}{3} n

Domain of

- 5 cos (3 x) - 2 : - \infty < x < \infty

Find intervals:

Increasing

: \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n,

Decreasing

: \frac{π}{3} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Plug the extreme point

x = \frac{2 π}{3} n

into

- 5 cos (3 x) - 2 \Rightarrow y = - 7

Minimum (\frac{2 π}{3} n, - 7)

Plug the extreme point

x = \frac{π}{3} + \frac{2 π}{3} n

into

- 5 cos (3 x) - 2 \Rightarrow y = 3

Maximum (\frac{π}{3} + \frac{2 π}{3} n, 3)

Minimum (\frac{2 π}{3} n, - 7), Maximum (\frac{π}{3} + \frac{2 π}{3} n, 3)

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