What is the extreme y=-9cos(3x) ?

The extreme y=-9cos(3x) is Minimum((2pi)/3 n,-9),Maximum(pi/3+(2pi)/3 n,9)

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extreme y=-9cos(3x)

extreme points

y = - 9 cos (3 x)

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

Solution steps

Find the critical points:

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

Domain of

- 9 cos (3 x) : - \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

- 9 cos (3 x) \Rightarrow y = - 9

Minimum (\frac{2 π}{3} n, - 9)

Plug the extreme point

x = \frac{π}{3} + \frac{2 π}{3} n

into

- 9 cos (3 x) \Rightarrow y = 9

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

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

4 x e^{x}

f (x) = \frac{8 + x}{8 - x}, 4 \leq x \leq 6

f (x) = - 1 + 4 (1 - x)^{2}

f (x) = 2 x^{3} - 7 x^{2} + 4 x

x^{4} + 2 x^{3} + x^{2} + x + 1

What is the extreme y=-9cos(3x) ?
The extreme y=-9cos(3x) is Minimum((2pi)/3 n,-9),Maximum(pi/3+(2pi)/3 n,9)