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tangent f(x)= x/(9-sqrt(x))

解答

切线

f (x) = \frac{x}{9 - x}

解答

y = \frac{18 - a _{0}}{2 ( 9 - a _{0} ) ^{2}} x - \frac{a _{0} a _{0}}{2 ( - a _{0} + 9 ) ^{2}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, \frac{a _{0} ( 9 + a _{0} )}{81 - a _{0}})

计算

f (x) = \frac{x}{9 - x}

的斜率:

\frac{df ( x )}{d x} = \frac{18 - x}{2 ( 9 - x ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{18 - a _{0}}{2 ( 9 - a _{0} ) ^{2}}

找到斜率 m=

\frac{18 - a _{0}}{2 ( 9 - a _{0} ) ^{2}}

且穿过

(a_{0}, \frac{a _{0} ( 9 + a _{0} )}{81 - a _{0}})

的直线:

y = \frac{18 - a _{0}}{2 ( 9 - a _{0} ) ^{2}} x - \frac{a _{0} a _{0}}{2 ( - a _{0} + 9 ) ^{2}}

y = \frac{18 - a _{0}}{2 ( 9 - a _{0} ) ^{2}} x - \frac{a _{0} a _{0}}{2 ( - a _{0} + 9 ) ^{2}}

作图

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