问题
填空题
已知函数y=f(x)(x∈R)上任意一点P(x0,f(x0))处的切线的斜率k=(x0-2)(x0-5)2,则该函数的单调减区间为______.
答案
由题意可知函数的导函数为f′(x)=(x0-2)(x0-5)2,
函数的单调减区间,即函数的导函数小于0即可,
因此使(x0-2)(x0-5)2<0,得x0<2,
故答案为:(-∞,2).
已知函数y=f(x)(x∈R)上任意一点P(x0,f(x0))处的切线的斜率k=(x0-2)(x0-5)2,则该函数的单调减区间为______.
由题意可知函数的导函数为f′(x)=(x0-2)(x0-5)2,
函数的单调减区间,即函数的导函数小于0即可,
因此使(x0-2)(x0-5)2<0,得x0<2,
故答案为:(-∞,2).
补全对话。 | |
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