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受欢迎的微积分 >

tangent f(x)=4x^3-42x^2+146x+48

解答

切线

f (x) = 4 x^{3} - 42 x^{2} + 146 x + 48

解答

y = (12 a_{0}^{2} - 84 a_{0} + 146) x - 8 a_{0}^{3} + 42 a_{0}^{2} + 48

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, 4 a_{0}^{3} - 42 a_{0}^{2} + 146 a_{0} + 48)

计算

f (x) = 4 x^{3} - 42 x^{2} + 146 x + 48

的斜率:

\frac{df ( x )}{d x} = 12 x^{2} - 84 x + 146

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 = 12 a_{0}^{2} - 84 a_{0} + 146

找到斜率 m=

12 a_{0}^{2} - 84 a_{0} + 146

且穿过

(a_{0}, 4 a_{0}^{3} - 42 a_{0}^{2} + 146 a_{0} + 48)

的直线:

y = (12 a_{0}^{2} - 84 a_{0} + 146) x - 8 a_{0}^{3} + 42 a_{0}^{2} + 48

y = (12 a_{0}^{2} - 84 a_{0} + 146) x - 8 a_{0}^{3} + 42 a_{0}^{2} + 48

作图

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