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受欢迎的函数 >

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

解答

极值点

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

解答

极小值 (- 1, \frac{1}{2}), 极大值 (- \frac{2}{3}, \frac{10}{9}), 极小值 (\frac{1}{3}, - \frac{7}{18}), 极大值 (1, \frac{5}{2})

求解步骤

找到临界点:

x = - 1, x = - \frac{2}{3}, x = \frac{1}{3}, x = 1

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

的定义域

: - 1 \leq x \leq 1

Find intervals:

递增

: - 1 < x < - \frac{2}{3},

递减

: - \frac{2}{3} < x < \frac{1}{3},

递增

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

将极值点

x = - 1

代入

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

极小值 (- 1, \frac{1}{2})

将极值点

x = - \frac{2}{3}

代入

3 x^{3} + \frac{3}{2} x^{2} - 2 x \Rightarrow y = \frac{10}{9}

极大值 (- \frac{2}{3}, \frac{10}{9})

将极值点

x = \frac{1}{3}

代入

3 x^{3} + \frac{3}{2} x^{2} - 2 x \Rightarrow y = - \frac{7}{18}

极小值 (\frac{1}{3}, - \frac{7}{18})

将极值点

x = 1

代入

3 x^{3} + \frac{3}{2} x^{2} - 2 x \Rightarrow y = \frac{5}{2}

极大值 (1, \frac{5}{2})

极小值 (- 1, \frac{1}{2}), 极大值 (- \frac{2}{3}, \frac{10}{9}), 极小值 (\frac{1}{3}, - \frac{7}{18}), 极大值 (1, \frac{5}{2})

作图

流行的例子

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