设函数f（x）=x2-1，对任意x∈[
|
依据题意得
-1-4m2(x2-1)≤(x-1)2-1+4(m2-1)在x∈[x2 m2
，+∞)上恒定成立，3 2
即
-4m2≤-1 m2
-3 x2
+1在x∈[2 x
，+∞)上恒成立．3 2
当x=
时，函数y=-3 2
-3 x2
+1取得最小值-2 x
，所以5 3
-4m2≤-1 m2
，即（3m2+1）（4m2-3）≥0，5 3
解得m≤-
或m≥3 2
，3 2
故答案为：（-∞，-
]∪[3 2
，+∞）．3 2
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| In the deserts of North Africa and Saudi Arabia lives the smallest of all foxes with the largest of ears. This animal is the fennec fox. Fennec foxes have ears that are 5 to 6 inches long. That's big for an animal that weighs less than four pounds. Their ears help shed (去除) body heat. And, as you may have guessed, they also provide great hearing. It's also interesting to think about the hair of fennec foxes. Why would a fox that lives in the desert need a thick, fur coat? Actually, the desert isn't always warm. During the nighttime, a desert can be terribly cold! A fennec fox's fur keeps them warm during those desert nights. They also have long bushy tails that they use as a blanket. And the hair on their feet protects them from the hot sand in the daytime. Fennec foxes live in small communities of dens (兽穴).They spend most of the day sleeping in their dens, out of the hot sun. Then, when night comes, they come out in search of food. In addition to their great hearing, fennecs also use their great sense of smell and big eyes to track down dinner. Like other foxes, fennecs are omnivores. This means they eat both meat and plants. They like eating birds, eggs, insects, snails, fruit and leaves best. Fennec fox mothers have one to five babies at a time. The lifespan of a fennec fox is 10 to 12 years. The cream coloration of fennec foxes help them blend into their desert habitat. Still, they have to watch out for predators (捕食性动物). These include caracals ( a type of wild cat ) , jackals, eagle owls, hyenas and humans. Humans catch them for their fur and to sell as pets. | |
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