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Beliebt Funktionen >

extreme 6sqrt(3cos(x)+6sin^2(x))

Lösung

extrempunkte

6 3 cos (x) + 6 sin^{2} (x)

Lösung

Minimum (2 πn, 6 3 cos (2 πn) + 6 sin^{2} (2 πn)), Sattel (arccos (\frac{1}{4}) + 2 πn, 6 3 cos (arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (arccos (\frac{1}{4}) + 2 πn)), Maximum (arccos (\frac{- 17 + 1}{4}), 0), Maximum (- arccos (\frac{- 17 + 1}{4}) + 2 π, 0), Sattel (2 π - arccos (\frac{1}{4}) + 2 πn, 6 3 cos (2 π - arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (2 π - arccos (\frac{1}{4}) + 2 πn))

Schritte zur Lösung

Bestimme den kritischen Punkt:

x = 2 πn, x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Bereich von

6 3 cos (x) + 6 sin^{2} (x) : - arccos (\frac{- 17 + 1}{4}) + 2 πn \leq x \leq arccos (\frac{- 17 + 1}{4}) + 2 πn

Intervalle finden:

Ansteigend

: 2 πn < x < arccos (\frac{1}{4}) + 2 πn,

Ansteigend

: arccos (\frac{1}{4}) + 2 πn < x < 2 π + 2 πn,

Absteigend

: 2 πn \leq x < 2 π - arccos (\frac{1}{4}) + 2 πn,

Absteigend

: 2 π - arccos (\frac{1}{4}) + 2 πn < x < 2 π + 2 πn

Setz die Extremwerte

x = 2 πn

in

6 3 cos (x) + 6 sin^{2} (x) \Rightarrow y = 6 3 cos (2 πn) + 6 sin^{2} (2 πn)

ein

Minimum (2 πn, 6 3 cos (2 πn) + 6 sin^{2} (2 πn))

Setz die Extremwerte

x = arccos (\frac{1}{4}) + 2 πn

in

6 3 cos (x) + 6 sin^{2} (x) \Rightarrow y = 6 3 cos (arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (arccos (\frac{1}{4}) + 2 πn)

ein

Sattel (arccos (\frac{1}{4}) + 2 πn, 6 3 cos (arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (arccos (\frac{1}{4}) + 2 πn))

Setz die Extremwerte

x = arccos (\frac{- 17 + 1}{4})

in

6 3 cos (x) + 6 sin^{2} (x) \Rightarrow y = 0

ein

Maximum (arccos (\frac{- 17 + 1}{4}), 0)

Setz die Extremwerte

x = - arccos (\frac{- 17 + 1}{4}) + 2 π

in

6 3 cos (x) + 6 sin^{2} (x) \Rightarrow y = 0

ein

Maximum (- arccos (\frac{- 17 + 1}{4}) + 2 π, 0)

Setz die Extremwerte

x = 2 π - arccos (\frac{1}{4}) + 2 πn

in

6 3 cos (x) + 6 sin^{2} (x) \Rightarrow y = 6 3 cos (2 π - arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (2 π - arccos (\frac{1}{4}) + 2 πn)

ein

Sattel (2 π - arccos (\frac{1}{4}) + 2 πn, 6 3 cos (2 π - arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (2 π - arccos (\frac{1}{4}) + 2 πn))

Minimum (2 πn, 6 3 cos (2 πn) + 6 sin^{2} (2 πn)), Sattel (arccos (\frac{1}{4}) + 2 πn, 6 3 cos (arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (arccos (\frac{1}{4}) + 2 πn)), Maximum (arccos (\frac{- 17 + 1}{4}), 0), Maximum (- arccos (\frac{- 17 + 1}{4}) + 2 π, 0), Sattel (2 π - arccos (\frac{1}{4}) + 2 πn, 6 3 cos (2 π - arccos (\frac{1}{4}) + 2 πn) + 6 sin^{2} (2 π - arccos (\frac{1}{4}) + 2 πn))

Graph

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