find-the-maximum-value-of-2-3cosh2x-2-

Question Number 84220 by Rio Michael last updated on 10/Mar/20

find the maximum value of \frac{2}{3 \cosh 2 x + 2}

Commented by mr W last updated on 10/Mar/20

\cosh 2 x ⩾ 1

3 \cosh 2 x + 2 ⩾ 3 \times 1 + 2 = 5

\frac{2}{3 \cosh 2 x + 2} ⩽ \frac{2}{5} = m a x i m u m

Answered by TANMAY PANACEA last updated on 10/Mar/20

\frac{2}{3 (\frac{e^{2 x} + e^{- 2 x}}{2}) + 2} = y

y = \frac{4}{3 e^{2 x} + 3 e^{- 2 x} + 4} = \frac{4}{3 a + \frac{3}{a} + 4} = \frac{4}{3 {{(\sqrt{a} - \frac{1}{\sqrt{a}})}^{2} + 2} + 4}

y_{m a x} = \frac{4}{3 (0 + 2) + 4} = \frac{4}{10} = \frac{2}{5}

Commented by Rio Michael last updated on 10/Mar/20

t h a n k s