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受欢迎的函数 >

extreme f(x)=x(15-48+2x)(48/2-x)

解答

极值点

f (x) = x (15 - 48 + 2 x) (\frac{48}{2} - x)

解答

极小值 (\frac{27 - 201}{2}, - \frac{3 ( 567 + 67 201 )}{2}), 极大值 (\frac{27 + 201}{2}, \frac{3 ( 67 201 - 567 )}{2})

求解步骤

f^{'} (x) = - 6 (x^{2} - 27 x + 132)

Find intervals:

递减

: - \infty < x < \frac{- 201 + 27}{2},

递增

: \frac{- 201 + 27}{2} < x < \frac{201 + 27}{2},

递减

: \frac{201 + 27}{2} < x < \infty

将

x = \frac{27 - 201}{2}

代入

x (15 - 48 + 2 x) (\frac{48}{2} - x) : - \frac{3 ( 567 + 67 201 )}{2}

极小值 (\frac{27 - 201}{2}, - \frac{3 ( 567 + 67 201 )}{2})

将

x = \frac{27 + 201}{2}

代入

x (15 - 48 + 2 x) (\frac{48}{2} - x) : \frac{3 ( 67 201 - 567 )}{2}

极大值 (\frac{27 + 201}{2}, \frac{3 ( 67 201 - 567 )}{2})

极小值 (\frac{27 - 201}{2}, - \frac{3 ( 567 + 67 201 )}{2}), 极大值 (\frac{27 + 201}{2}, \frac{3 ( 67 201 - 567 )}{2})

作图

流行的例子

extreme f(x)=x^2+y^2+4x-2y+6

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extreme (2-x)/(x+4)

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