若函数f(x)＝x3－3x－a在区间[0,3]上的最大值、最小值分别为M、N，则M－N的值为 ( )
A．2
B．4
C．18
D．20
答案：D
分析：因为要求函数的最大值和最小值，先求出函数的导函数f′（x）=3x2-3，然后令f′（x）=3x2-3=0得x=±1，又因为函数在区间[0，3]取最值，所以要讨论x的两个范围0≤x＜1和1≤x≤3时f′（x）的正与负，因为0≤x＜1时，f′（x）＜0；1≤x≤3时，f′（x）＞0所以f（1）最小，最大值要看区间的两个端点即f（3）和f（0），判断其谁大谁就是最大值，则就求出了M和N，解出M-N即可．
解：f′（x）=3x2-3，令f′（x）=0得x=±1．
当0≤x＜1时，f′（x）＜0；当1≤x≤3时，f′（x）＞0．则f（1）最小，则N=f（1）
又f（0）=-a，f（3）=18-a，
又f（3）＞f（0），∴最大值为f（3），即M=f（3），
所以M-N=f（3）-f（1）=（18-a）-（-2-a）=20．
故答案为D．
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