What is the extreme 4cos(3x)+5 ?

The extreme 4cos(3x)+5 is Maximum((2pi)/3 n,9),Minimum(pi/3+(2pi)/3 n,1)

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extreme 4cos(3x)+5

extreme points

4 cos (3 x) + 5

Maximum (\frac{2 π}{3} n, 9), Minimum (\frac{π}{3} + \frac{2 π}{3} n, 1)

Solution steps

Find the critical points:

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

Domain of

4 cos (3 x) + 5 : - \infty < x < \infty

Find intervals:

Decreasing

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

Increasing

: \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

4 cos (3 x) + 5 \Rightarrow y = 9

Maximum (\frac{2 π}{3} n, 9)

Plug the extreme point

x = \frac{π}{3} + \frac{2 π}{3} n

into

4 cos (3 x) + 5 \Rightarrow y = 1

Minimum (\frac{π}{3} + \frac{2 π}{3} n, 1)

Maximum (\frac{2 π}{3} n, 9), Minimum (\frac{π}{3} + \frac{2 π}{3} n, 1)

f (x) = \frac{e ^{x}}{x ^{8}}

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

f (x) = x^{3} - \frac{27}{2} x^{2} + 42 x + 1

f (x) = - 2 x 3 - x

f (x) = 1.1 x^{4} - 5.1 x^{2} + 4.07

What is the extreme 4cos(3x)+5 ?
The extreme 4cos(3x)+5 is Maximum((2pi)/3 n,9),Minimum(pi/3+(2pi)/3 n,1)