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受欢迎的微积分 >

tangent (2x+3)^{1/4}

解答

切线

(2 x + 3)^{\frac{1}{4}}

解答

y = \frac{1}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}} x + (2 a_{0} + 3)^{\frac{1}{4}} - \frac{a _{0}}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, (2 a_{0} + 3)^{\frac{1}{4}})

计算

y = (2 x + 3)^{\frac{1}{4}}

的斜率:

\frac{d y}{d x} = \frac{1}{2 ( 2 x + 3 ) ^{\frac{3}{4}}}

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{1}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}}

找到斜率 m=

\frac{1}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}}

且穿过

(a_{0}, (2 a_{0} + 3)^{\frac{1}{4}})

的直线:

y = \frac{1}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}} x + (2 a_{0} + 3)^{\frac{1}{4}} - \frac{a _{0}}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}}

y = \frac{1}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}} x + (2 a_{0} + 3)^{\frac{1}{4}} - \frac{a _{0}}{2 ( 2 a _{0} + 3 ) ^{\frac{3}{4}}}

作图

流行的例子

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a re a y^{2} + 8 x = 16, y^{2} - 24 x = 48

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