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Beliebt Rechnen >

tangent y=(x^2)/(x-8),(2, 2/5)

Lösung

tangente von

y = \frac{x ^{2}}{x - 8}, (2, \frac{2}{5})

Lösung

y = - \frac{43 + 16 10}{45} x + \frac{2}{5} + \frac{2 ( 43 + 16 10 )}{45} or y = \frac{16 10 - 43}{45} x + \frac{2}{5} - \frac{2 ( 16 10 - 43 )}{45}

Schritte zur Lösung

Steigung der Tangente an

(2, \frac{2}{5}) : m = \frac{5 x ^{2} - 2 ( x - 8 )}{5 ( x - 8 ) ( x - 2 )}

Finde die Steigung von

y = \frac{x ^{2}}{x - 8} : m = \frac{x ^{2} - 16 x}{( x - 8 ) ^{2}}

Löse

\frac{x ^{2} - 16 x}{( x - 8 ) ^{2}} = \frac{5 x ^{2} - 2 ( x - 8 )}{5 ( x - 8 ) ( x - 2 )} : x = \frac{2 ( 2 + 10 )}{3}, x = \frac{2 ( 2 - 10 )}{3}

Finde die Tangente an

x = \frac{2 ( 2 + 10 )}{3} : y = - \frac{43 + 16 10}{45} x + \frac{2}{5} + \frac{2 ( 43 + 16 10 )}{45}

Finde die Tangente an

x = \frac{2 ( 2 - 10 )}{3} : y = \frac{16 10 - 43}{45} x + \frac{2}{5} - \frac{2 ( 16 10 - 43 )}{45}

y = - \frac{43 + 16 10}{45} x + \frac{2}{5} + \frac{2 ( 43 + 16 10 )}{45} or y = \frac{16 10 - 43}{45} x + \frac{2}{5} - \frac{2 ( 16 10 - 43 )}{45}

Graph

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