Find-maximum-and-minimum-value-of-function-f-x-27-cos-2x-81-sin-2x-

Question Number 128753 by bramlexs22 last updated on 10/Jan/21

Find maximum and minimum

value of function f (x) = 27^{\cos 2 x} . 81^{\sin 2 x} ?

Answered by liberty last updated on 10/Jan/21

\Leftrightarrow f (x) = 3^{3 \cos 2 x} . 3^{4 \sin 2 x}

f (x) = 3^{3 \cos 2 x + 4 \sin 2 x} = 3^{5 \cos (2 x - α)}

we know that - 1 ⩽ \cos (2 x - α) ⩽ 1 it follows

that \max f (x) = 3^{5.1} = 3^{5} = 243 and minimum

f (x) = 3^{5 . (- 1)} = 3^{- 5} = \frac{1}{243} .

Facebook Tweet Pin