Question

求方程2x-3+根号下13-4x的最值

Answer 1

t = (13-4x)^(1/2)>=0,

t^2 = 13-4x,2x = (13-t^2)/2,

f(t) = (13-t^2)/2 - 3 + t = [7 + 2t - t^2]/2,

f'(t) = (2-2t)/2=1-t,

0=0时,f(t)只有最大值.f(t)在t=1时达到最大值4.

此时,2x = (13-1)/2 = 6,x = 3.

因此,2x-3+根号下13-4x在x=3时达到最大值4.【2x-3+根号下13-4x没有最小值】