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受欢迎的函数 >

extreme f(x)=(1/(x^3-2x^2)),1<= x<= 7/5

解答

极值点

f (x) = (\frac{1}{x ^{3} - 2 x ^{2}}), 1 \leq x \leq \frac{7}{5}

解答

极小值 (1, - 1), 极大值 (\frac{4}{3}, - \frac{27}{32}), 极小值 (\frac{7}{5}, - \frac{125}{147})

求解步骤

找到临界点:

x = 1, x = \frac{4}{3}, x = \frac{7}{5}

\frac{1}{x ^{3} - 2 x ^{2}}, 1 \leq x \leq \frac{7}{5}

的定义域

: 1 \leq x \leq \frac{7}{5}

Find intervals:

递增

: 1 < x < \frac{4}{3},

递减

: \frac{4}{3} < x < \frac{7}{5}

将极值点

x = 1

代入

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

极小值 (1, - 1)

将极值点

x = \frac{4}{3}

代入

\frac{1}{x ^{3} - 2 x ^{2}} \Rightarrow y = - \frac{27}{32}

极大值 (\frac{4}{3}, - \frac{27}{32})

将极值点

x = \frac{7}{5}

代入

\frac{1}{x ^{3} - 2 x ^{2}} \Rightarrow y = - \frac{125}{147}

极小值 (\frac{7}{5}, - \frac{125}{147})

极小值 (1, - 1), 极大值 (\frac{4}{3}, - \frac{27}{32}), 极小值 (\frac{7}{5}, - \frac{125}{147})

作图

流行的例子

extreme e^{-(x^2+y^2)}(x^2+2y^2)

e x t re m e e^{- (x^{2} + y^{2})} (x^{2} + 2 y^{2})

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e x t re m e \frac{1}{3} x^{3} + 2 x + 4 x + 1

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