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受欢迎的微积分 >

tangent f(x)=2x^3+3x^2-12x+1

解答

切线

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 1

解答

y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 1

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} + 3 a_{0}^{2} - 12 a_{0} + 1)

计算

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 1

的斜率:

\frac{df ( x )}{d x} = 6 x^{2} + 6 x - 12

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 = 6 a_{0}^{2} + 6 a_{0} - 12

找到斜率 m=

6 a_{0}^{2} + 6 a_{0} - 12

且穿过

(a_{0}, 2 a_{0}^{3} + 3 a_{0}^{2} - 12 a_{0} + 1)

的直线:

y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 1

y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 1

作图

流行的例子

(d^2y)/(dx^2)=4xcos(x^2)

\frac{d ^{2} y}{d x ^{2}} = 4 x cos (x^{2})

3y^'+y=(1-2x)y^4

3 y^{^{'}} + y = (1 - 2 x) y^{4}

y = \frac{- 1}{3 x ^{2}}

derivative of 3sqrt(x)-4x^3+2^x-e+7

\frac{d}{d x} (3 x - 4 x^{3} + 2^{x} - e + 7)

tangent y=sqrt(1+x^3),(2,3)

t an g e n t y = 1 + x^{3}, (2, 3)