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Beliebt Funktionen >

extreme f(x)=x^{4/5}(x-9)^2

Lösung

extrempunkte

f (x) = x^{\frac{4}{5}} (x - 9)^{2}

Lösung

Minimum (0, 0), Maximum (\frac{18}{7}, \frac{2025 \cdot 1 8 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}), Minimum (9, 0)

Schritte zur Lösung

f^{'} (x) = \frac{2 ( 7 x - 18 ) ( - 9 + x )}{5 x ^{\frac{1}{5}}}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{18}{7},

Absteigend

: \frac{18}{7} < x < 9,

Ansteigend

: 9 < x < \infty

Stecke

x = 0

in

x^{\frac{4}{5}} (x - 9)^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{18}{7}

in

x^{\frac{4}{5}} (x - 9)^{2} : \frac{2025 \cdot 1 8 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}

Maximum (\frac{18}{7}, \frac{2025 \cdot 1 8 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}})

Stecke

x = 9

in

x^{\frac{4}{5}} (x - 9)^{2} : 0

Minimum (9, 0)

Minimum (0, 0), Maximum (\frac{18}{7}, \frac{2025 \cdot 1 8 ^{\frac{4}{5}}}{49 \cdot 7 ^{\frac{4}{5}}}), Minimum (9, 0)

Graph

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