What is the extreme 18cos(θ)+9sin^2(θ),-pi<= θ<= pi ?

The extreme 18cos(θ)+9sin^2(θ),-pi<= θ<= pi is Minimum(-pi,-18),Maximum(0,18),Minimum(pi,-18)

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extreme 18cos(θ)+9sin^2(θ),-pi<= θ<= pi

extreme points

18 cos (θ) + 9 sin^{2} (θ), - π \leq θ \leq π

Minimum (- π, - 18), Maximum (0, 18), Minimum (π, - 18)

Solution steps

Find the critical points:

θ = - π, θ = 0, θ = π

Domain of

18 cos (θ) + 9 sin^{2} (θ), - π \leq θ \leq π : - π \leq θ \leq π

Find intervals:

Increasing

: - π < θ < 0,

Decreasing

: 0 < θ < π

Plug the extreme point

x = - π

into

18 cos (θ) + 9 sin^{2} (θ) \Rightarrow y = - 18

Minimum (- π, - 18)

Plug the extreme point

x = 0

into

18 cos (θ) + 9 sin^{2} (θ) \Rightarrow y = 18

Maximum (0, 18)

Plug the extreme point

x = π

into

18 cos (θ) + 9 sin^{2} (θ) \Rightarrow y = - 18

Minimum (π, - 18)

Minimum (- π, - 18), Maximum (0, 18), Minimum (π, - 18)

f (x, y) = x^{2} - 2 x + \frac{y ^{2}}{2} - 2 y

y = x^{4} - 2 x^{3}

f (x) = \frac{( x ^{2} + x + 4 )}{3 + x ^{2}}

f (x) = x^{3} - 6 x + 9 x - 2

f (x) = x^{3} - 12 x, 0 \leq x \leq 5

What is the extreme 18cos(θ)+9sin^2(θ),-pi<= θ<= pi ?
The extreme 18cos(θ)+9sin^2(θ),-pi<= θ<= pi is Minimum(-pi,-18),Maximum(0,18),Minimum(pi,-18)