Question

求函数f(x)=log(1/2) 2 x-log(1/4) x +5在x∈[2,4]的最大值何最小值

Answer 1

f(x)=log(1/2) 2 x-log(1/4) x +5

=log(1/2) 2 x-log(1/2) (x^(1/2))+5

=log(1/2)(2x/√x)+5

=log(1/2)(2√x)+5

因为x∈[2,4]

log(1/2)(2√x)∈[-2,-3/2]

log(1/2)(2√x)+5∈[3,7/2]

所以最大值和最小值分别是7/2和3