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受欢迎的函数 >

extreme f(x)=x^3+2x^2-3x

解答

极值点

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

解答

极大值 (- \frac{2 + 13}{3}, 13 + \frac{16 - 13}{27} + 2), 极小值 (\frac{- 2 + 13}{3}, 2 - 13 + \frac{16 + 13}{27})

求解步骤

f^{'} (x) = 3 x^{2} + 4 x - 3

Find intervals:

递增

: - \infty < x < \frac{- 13 - 2}{3},

递减

: \frac{- 13 - 2}{3} < x < \frac{13 - 2}{3},

递增

: \frac{13 - 2}{3} < x < \infty

将

x = - \frac{2 + 13}{3}

代入

x^{3} + 2 x^{2} - 3 x : 13 + \frac{16 - 13}{27} + 2

极大值 (- \frac{2 + 13}{3}, 13 + \frac{16 - 13}{27} + 2)

将

x = \frac{- 2 + 13}{3}

代入

x^{3} + 2 x^{2} - 3 x : 2 - 13 + \frac{16 + 13}{27}

极小值 (\frac{- 2 + 13}{3}, 2 - 13 + \frac{16 + 13}{27})

极大值 (- \frac{2 + 13}{3}, 13 + \frac{16 - 13}{27} + 2), 极小值 (\frac{- 2 + 13}{3}, 2 - 13 + \frac{16 + 13}{27})

作图

流行的例子

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