माना `f(x)` = `|[1+sin^2 x , cos^2 x, sin^2x],[sin^2x , 1+cos^2x ,sin 2x], [sin^2x ,cos^2x , 1 + sin 2x]|`, `x in [frac {pi}{6}, frac{pi}{3}]` है | यदि f के अधिकतम व न्यूनतम मान क्रमशः `alpha व beta` है तब,

Options

A. `alpha^2 + beta^2 = 9/2`
B. `beta^2 + 2 sqrt alpha = (19)/4`
C. `alpha^2 - beta^2 = 4 sqrt 3`
D. `beta^2 - 2 sqrt alpha = (19/4)`