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受欢迎的微积分 >

tangent 9x^{1/2}+x^{3/2}

解答

切线

9 x^{\frac{1}{2}} + x^{\frac{3}{2}}

解答

y = (\frac{9}{2 a _{0}^{\frac{1}{2}}} + \frac{3 a _{0}^{\frac{1}{2}}}{2}) x + 9 a_{0}^{\frac{1}{2}} + a_{0}^{\frac{3}{2}} + \frac{- 9 a _{0}^{\frac{1}{2}} - 3 a _{0}^{\frac{3}{2}}}{2}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, 9 a_{0}^{\frac{1}{2}} + a_{0}^{\frac{3}{2}})

计算

y = 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}

的斜率:

\frac{d y}{d x} = \frac{9}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{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{9}{2 a _{0}^{\frac{1}{2}}} + \frac{3 a _{0}^{\frac{1}{2}}}{2}

找到斜率 m=

\frac{9}{2 a _{0}^{\frac{1}{2}}} + \frac{3 a _{0}^{\frac{1}{2}}}{2}

且穿过

(a_{0}, 9 a_{0}^{\frac{1}{2}} + a_{0}^{\frac{3}{2}})

的直线:

y = (\frac{9}{2 a _{0}^{\frac{1}{2}}} + \frac{3 a _{0}^{\frac{1}{2}}}{2}) x + 9 a_{0}^{\frac{1}{2}} + a_{0}^{\frac{3}{2}} + \frac{- 9 a _{0}^{\frac{1}{2}} - 3 a _{0}^{\frac{3}{2}}}{2}

y = (\frac{9}{2 a _{0}^{\frac{1}{2}}} + \frac{3 a _{0}^{\frac{1}{2}}}{2}) x + 9 a_{0}^{\frac{1}{2}} + a_{0}^{\frac{3}{2}} + \frac{- 9 a _{0}^{\frac{1}{2}} - 3 a _{0}^{\frac{3}{2}}}{2}

作图

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