what is the maximum value of??

f(x) = (1/2)^y where y = x² - 3x +2

Taking log on both sides,

ln f(x) = (x² - 3x +2) ln (1/2)

Differentiating on both sides,

(1/f(x)) df(x)/dx = (2x -3) ln (1/2)

For the maximum value of the function,

df(x)/dx = 0

df(x)/dx = 0

(2x-3) = 0

x = 3/2

y = -1/4

Hence f(3/2) = (1/2)^-1/4 = (2)^1/4

Regards,

Team,

TopperLearning.