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受欢迎的微积分 >

tangent f(x)=(x-4)(3-x)^3

解答

切线

f (x) = (x - 4) (3 - x)^{3}

解答

y = (- 4 a_{0}^{3} + 39 a_{0}^{2} - 126 a_{0} + 135) x + 3 a_{0}^{4} - 26 a_{0}^{3} + 63 a_{0}^{2} - 108

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, (a_{0} - 4) (3 - a_{0})^{3})

计算

f (x) = (x - 4) (3 - x)^{3}

的斜率:

\frac{df ( x )}{d x} = (3 - x)^{3} - 3 (3 - x)^{2} (x - 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 = - 4 a_{0}^{3} + 39 a_{0}^{2} - 126 a_{0} + 135

找到斜率 m=

- 4 a_{0}^{3} + 39 a_{0}^{2} - 126 a_{0} + 135

且穿过

(a_{0}, (a_{0} - 4) (3 - a_{0})^{3})

的直线:

y = (- 4 a_{0}^{3} + 39 a_{0}^{2} - 126 a_{0} + 135) x + 3 a_{0}^{4} - 26 a_{0}^{3} + 63 a_{0}^{2} - 108

y = (- 4 a_{0}^{3} + 39 a_{0}^{2} - 126 a_{0} + 135) x + 3 a_{0}^{4} - 26 a_{0}^{3} + 63 a_{0}^{2} - 108

作图

流行的例子

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x \to 0 + lim (x)

y^'+y=e^xsin(e^x)

y^{^{'}} + y = e^{x} sin (e^{x})

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