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受欢迎的函数 >

f(x)=(3x^3-9x^2-6x+1}{\frac{x^2)/3+7x-8}

解答

f (x) = \frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

解答

Domain : x < \frac{- 21 - 537}{2} or \frac{- 21 - 537}{2} < x < \frac{- 21 + 537}{2} or x > \frac{- 21 + 537}{2}

Range : - \infty < f (x) < \infty

X 截距 : (0.13902 \dots, 0), (- 0.67759 \dots, 0), (3.53857 \dots, 0), Y 截距 : (0, - \frac{1}{8})

Asymptotes : 垂直 x = \frac{- 21 - 537}{2}, x = \frac{- 21 + 537}{2}, Slant y = 9 x - 216

Extreme Points : 极大值 (- 45.02422 \dots, - 827.63897 \dots), 极小值 (- 0.23231 \dots, - 0.19468 \dots)

+1

间隔符号

Domain : (- \infty, \frac{- 21 - 537}{2}) \cup (\frac{- 21 - 537}{2}, \frac{- 21 + 537}{2}) \cup (\frac{- 21 + 537}{2}, \infty)

Range : (- \infty, \infty)

求解步骤

\frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

的定义域

: x < \frac{- 21 - 537}{2} or \frac{- 21 - 537}{2} < x < \frac{- 21 + 537}{2} or x > \frac{- 21 + 537}{2}

\frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

的值域:

- \infty < f (x) < \infty

\frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

的轴截距点

:

X 截距

: (0.13902 \dots, 0), (- 0.67759 \dots, 0), (3.53857 \dots, 0),

Y 截距

: (0, - \frac{1}{8})

\frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

的渐近线

:

垂直

: x = \frac{- 21 - 537}{2}, x = \frac{- 21 + 537}{2},

Slant

: y = 9 x - 216

\frac{3 x ^{3} - 9 x ^{2} - 6 x + 1}{\frac{x ^{2}}{3} + 7 x - 8}

的极值点:

极大值

(- 45.02422 \dots, - 827.63897 \dots),

极小值

(- 0.23231 \dots, - 0.19468 \dots)

作图

流行的例子

f(x)=x^3-13x^2+59x-87

f (x) = x^{3} - 13 x^{2} + 59 x - 87

g(x)=(x-1)^4+4x^3-6x^2+4x-x^4

g (x) = (x - 1)^{4} + 4 x^{3} - 6 x^{2} + 4 x - x^{4}

p(t)=45*(1.18)^t

p (t) = 45 \cdot (1.18)^{t}

f (x) = x^{2} - 4 x - 91

y= 1/(1+e^{-x)}

y = \frac{1}{1 + e ^{- x}}