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易错点1端点值处最易出错的三种情形1.一元二次不等式恒成立类问题例如:设(fx)=x2-2ax+2ax+2(a∈R),若当x∈R时,不等试f(x)≥a恒成立,求a的取值范围.分析:当x∈R时,f(x)≥a恒成立,即当x∈R时,x2-2ax+2-a≥0恒成立。∴△=4a2-4(2-a)≤0(易错为)△<0),所以-2≤a≤1。2.使用最值原理时的端点值问题例如:若k>13x3-4x当x∈(2,3)恒成立,求k的取值范围。分析:由导数分析可知,当x∈(2,3)时f(x)=13x3-4x单调递增,故k应大于f(x)的最大值,而由于
Error-prone point 1 Endpoint value of the three most error-prone situations 1. Uniform quadratic inequalities Forming a class of problems For example: Let (fx) = x2-2ax +2 ax +2 (a∈R), if x∈R (X) ≥a constant holds, that is, when x∈R, x2-2ax + 2- a ≥ 0 constant established. ∴ △ = 4a2-4 (2-a) ≤ 0 (easy to be wrong) △ <0), so -2≤a≤1.2 Endpoint value problem when using the principle of the most value Example: If k> 13x3-4x When x∈ (2,3) holds, find the range of k. Analysis: According to the derivative analysis, f (x) = 13x3-4x monotonically increases when x∈ (2,3), so k should be greater than the maximum value of f (x)