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tangent f(x)=x^2(4-x)^2,\at x=1

解答

切线

f (x) = x^{2} (4 - x)^{2}, at x = 1

解答

y = 12 x - 3

求解步骤

找到切点:

(1, 9)

计算

f (x) = x^{2} (4 - x)^{2}

的斜率:

\frac{df ( x )}{d x} = 4 x^{3} - 24 x^{2} + 32 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 = 12

找到斜率 m=

12

且穿过

(1, 9)

的直线:

y = 12 x - 3

y = 12 x - 3

作图

流行的例子

limit as x approaches infinity of sqrt((12x^3-4x+1)/(1+3x+2x^3))

x \to \infty lim (\frac{12 x ^{3} - 4 x + 1}{1 + 3 x + 2 x ^{3}})

integral from-3 to 3 of |x|-(x^2-6)

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

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\int_{5}^{6} \frac{x}{x - 5} d x

integral of (x^2)/(x+5)

\int \frac{x ^{2}}{x + 5} d x

integral of (x-3)/(x^3+3x^2+2x)

\int \frac{x - 3}{x ^{3} + 3 x ^{2} + 2 x} d x