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受欢迎的函数 >

extreme f(x)=x^2-x-3,0<= x<= 3

解答

极值点

f (x) = x^{2} - x - 3, 0 \leq x \leq 3

解答

极大值 (0, - 3), 极小值 (\frac{1}{2}, - \frac{13}{4}), 极大值 (3, 3)

求解步骤

找到临界点:

x = 0, x = \frac{1}{2}, x = 3

x^{2} - x - 3, 0 \leq x \leq 3

的定义域

: 0 \leq x \leq 3

Find intervals:

递减

: 0 < x < \frac{1}{2},

递增

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

将极值点

x = 0

代入

x^{2} - x - 3 \Rightarrow y = - 3

极大值 (0, - 3)

将极值点

x = \frac{1}{2}

代入

x^{2} - x - 3 \Rightarrow y = - \frac{13}{4}

极小值 (\frac{1}{2}, - \frac{13}{4})

将极值点

x = 3

代入

x^{2} - x - 3 \Rightarrow y = 3

极大值 (3, 3)

极大值 (0, - 3), 极小值 (\frac{1}{2}, - \frac{13}{4}), 极大值 (3, 3)

作图

流行的例子

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