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受欢迎的函数 >

f(n)=4n^{12}-32n^7+48n^2

解答

f (n) = 4 n^{12} - 32 n^{7} + 48 n^{2}

解答

Domain : - \infty < n < \infty

Range : f (x) \geq 4 (\frac{7 + 31}{3})^{\frac{12}{5}} - 32 (\frac{7 + 31}{3})^{\frac{7}{5}} + 48 (\frac{7 + 31}{3})^{\frac{2}{5}}

X 截距 : (0, 0), (56, 0), (52, 0), Y 截距 : (0, 0)

Asymptotes : 无

Extreme Points : 极小值 (0, 0), 极大值 5 \frac{7 - 31}{3}, 4 (\frac{7 - 31}{3})^{\frac{12}{5}} - 32 (\frac{7 - 31}{3})^{\frac{7}{5}} + 48 (\frac{7 - 31}{3})^{\frac{2}{5}}, 极小值 5 \frac{7 + 31}{3}, 4 (\frac{7 + 31}{3})^{\frac{12}{5}} - 32 (\frac{7 + 31}{3})^{\frac{7}{5}} + 48 (\frac{7 + 31}{3})^{\frac{2}{5}}

+1

间隔符号

Domain : (- \infty, \infty)

Range : 4 (\frac{7 + 31}{3})^{\frac{12}{5}} - 32 (\frac{7 + 31}{3})^{\frac{7}{5}} + 48 (\frac{7 + 31}{3})^{\frac{2}{5}}, \infty

求解步骤

4 n^{12} - 32 n^{7} + 48 n^{2}

的定义域

: - \infty < n < \infty

4 n^{12} - 32 n^{7} + 48 n^{2}

的值域:

f (x) \geq 4 (\frac{7 + 31}{3})^{\frac{12}{5}} - 32 (\frac{7 + 31}{3})^{\frac{7}{5}} + 48 (\frac{7 + 31}{3})^{\frac{2}{5}}

4 n^{12} - 32 n^{7} + 48 n^{2}

的轴截距点

:

X 截距

: (0, 0), (56, 0), (52, 0),

Y 截距

: (0, 0)

4 n^{12} - 32 n^{7} + 48 n^{2}

的渐近线

:

无

4 n^{12} - 32 n^{7} + 48 n^{2}

的极值点:

极小值

(0, 0),

极大值

5 \frac{7 - 31}{3}, 4 (\frac{7 - 31}{3})^{\frac{12}{5}} - 32 (\frac{7 - 31}{3})^{\frac{7}{5}} + 48 (\frac{7 - 31}{3})^{\frac{2}{5}},

极小值

5 \frac{7 + 31}{3}, 4 (\frac{7 + 31}{3})^{\frac{12}{5}} - 32 (\frac{7 + 31}{3})^{\frac{7}{5}} + 48 (\frac{7 + 31}{3})^{\frac{2}{5}}

作图

流行的例子

f (y) = 3^{2 - y}

f(x)=ln(arctan(x))

f (x) = ln (arctan (x))

y = - \frac{1}{4} x

f(x)=-3(x+1)^2+5

f (x) = - 3 (x + 1)^{2} + 5

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