作业帮35,36题求完整过程,
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35,36题求完整过程,
35.e^x = t,x = lnt,f(e^x) = f(t) = (lnt)^2 - 2lnt + 3 = (lnt - 1)^2 + 2 = (ln (t/e))^2 + 2
f(x) = (ln(x/e))^2 + 2,x = e,f(e) = 2 为最小值
36.定义域（1,p)
f(x) = log_2_ (x+1)*(p-x)
(x+1)(p-x) = -x^2 + (p-1)x + p = p + (p-1)^2 /4 -(x - (p-1)/2)^2 = (p+1)^2 / 4 - (x-(p-1)/2)^2
当 x = (p-1)/2 时,f(x) 有最大值 2log_2_(p+1) - 2