她oo
幼苗
共回答了18个问题采纳率:88.9% 举报
f(x)=cos2x+sin2x=√2[(sin2x)*(√2/2)+(cos2x)*(√2/2)]
=√2[sin2xcos(π/4)+cos2xsin(π/4)]
=√2sin(2x+π/4)
-π/8≤x≤π/2 ==> 0≤2x+π/4≤5π/4
-√2/2≤sin(2x+π/4)≤1 ==> -1 ≤ f(x) ≤ √2
f(MAX)=√2 当且仅当 2x+π/4=π/2+2kπ 即x=π/8+kπ 时取“=”本题是x=π/8
f(min) =-1 当且仅当 2x+π/4=5π/4+2kπ 即x=π/2+kπ 时取“=”本题是x=π/2
1年前
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