extreme y=6xsqrt(36-x^2)

Lösung

extrempunkte

y = 6 x 36 - x^{2}

Maximum (- 6, 0), Minimum (- 32, - 108), Maximum (32, 108), Minimum (6, 0)

Schritte zur Lösung

f^{'} (x) = \frac{6 ( - 2 x ^{2} + 36 )}{36 - x ^{2}}

Intervalle finden:

Absteigend

: - 6 < x < - 32,

Ansteigend

: - 32 < x < 32,

Absteigend

: 32 < x < 6

Stecke

x = - 6

6 x 36 - x^{2} : 0

Maximum (- 6, 0)

Stecke

x = - 32

6 x 36 - x^{2} : - 108

Minimum (- 32, - 108)

Stecke

x = 32

6 x 36 - x^{2} : 108

Maximum (32, 108)

Stecke

x = 6

6 x 36 - x^{2} : 0

Minimum (6, 0)

Maximum (- 6, 0), Minimum (- 32, - 108), Maximum (32, 108), Minimum (6, 0)

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