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受欢迎的函数 >

extreme f(x)=x^3-2x^2-15x+52.2

解答

极值点

f (x) = x^{3} - 2 x^{2} - 15 x + 52.2

解答

极大值 (- \frac{5}{3}, 67.01481 \dots), 极小值 (3, 16.2)

求解步骤

f^{'} (x) = 3 x^{2} - 4 x - 15

Find intervals:

递增

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

递减

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

递增

: 3 < x < \infty

将

x = - \frac{5}{3}

代入

x^{3} - 2 x^{2} - 15 x + 52.2 : 67.01481 \dots

极大值 (- \frac{5}{3}, 67.01481 \dots)

将

x = 3

代入

x^{3} - 2 x^{2} - 15 x + 52.2 : 16.2

极小值 (3, 16.2)

极大值 (- \frac{5}{3}, 67.01481 \dots), 极小值 (3, 16.2)

作图

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