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受欢迎的函数 >

extreme f(x)=4-x^3+5x

解答

极值点

f (x) = 4 - x^{3} + 5 x

解答

极小值 (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}), 极大值 (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

求解步骤

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

Find intervals:

递减

: - \infty < x < - \frac{5}{3},

递增

: - \frac{5}{3} < x < \frac{5}{3},

递减

: \frac{5}{3} < x < \infty

将

x = - \frac{5}{3}

代入

4 - x^{3} + 5 x : 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}

极小值 (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3})

将

x = \frac{5}{3}

代入

4 - x^{3} + 5 x : 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3}

极大值 (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

极小值 (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}), 极大值 (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

作图

流行的例子

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e x t re m e f (x) = 2 x^{3} - 6 x + 11

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e x t re m e f (x) = sin (5 x), 0 \leq x \leq \frac{2 π}{5}

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