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受欢迎的微积分 >

tangent f(x)=((x-4))/(sqrt(x)-2)

解答

切线

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

解答

y = \frac{a _{0} - 4 a _{0} + 4}{2 a _{0} ( a _{0} - 2 ) ^{2}} x + a_{0} + 2 - \frac{a _{0} ( a _{0} - 4 a _{0} + 4 )}{2 ( a _{0} - 2 ) ^{2}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, a_{0} + 2)

计算

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

的斜率:

\frac{df ( x )}{d x} = \frac{x - 4 x + 4}{2 x ( x - 2 ) ^{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{a _{0} - 4 a _{0} + 4}{2 a _{0} ( a _{0} - 2 ) ^{2}}

找到斜率 m=

\frac{a _{0} - 4 a _{0} + 4}{2 a _{0} ( a _{0} - 2 ) ^{2}}

且穿过

(a_{0}, a_{0} + 2)

的直线:

y = \frac{a _{0} - 4 a _{0} + 4}{2 a _{0} ( a _{0} - 2 ) ^{2}} x + a_{0} + 2 - \frac{a _{0} ( a _{0} - 4 a _{0} + 4 )}{2 ( a _{0} - 2 ) ^{2}}

y = \frac{a _{0} - 4 a _{0} + 4}{2 a _{0} ( a _{0} - 2 ) ^{2}} x + a_{0} + 2 - \frac{a _{0} ( a _{0} - 4 a _{0} + 4 )}{2 ( a _{0} - 2 ) ^{2}}

作图

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