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受欢迎的微积分 >

tangent f(x)=x^4-10x^2+9

解答

切线

f (x) = x^{4} - 10 x^{2} + 9

解答

y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

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} - 10 a_{0}^{2} + 9)

计算

f (x) = x^{4} - 10 x^{2} + 9

的斜率:

\frac{df ( x )}{d x} = 4 x^{3} - 20 x

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} - 20 a_{0}

找到斜率 m=

4 a_{0}^{3} - 20 a_{0}

且穿过

(a_{0}, a_{0}^{4} - 10 a_{0}^{2} + 9)

的直线:

y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

作图

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