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Maximum value of 12sinx-9sin^2x......,....................... Is??......

Maximum value of 12sinx-9sin^2x......,....................... Is??......

Grade:11

3 Answers

Vikas TU
14149 Points
7 years ago
M = 12sinx-9sin^2x
Differentiate it w.r.t. x
dM/dx = 0 = 12cosx – 9sin2x
or
4cosx – 3sin2x = 0
2cosx  – 3sinxcosx = 0
cosx(2 – 3sinx) = 0
cosx = 0  and   sinx = 2/3 
x = pi/2  
 
Put pi/2 as x once and as sinx = 2/3
the value at mximum will be the answer.
jagdish singh singh
173 Points
7 years ago
\hspace{-0.58 cm}$Given $12\sin x-9\sin^2 x=3\sin x(4-3\sin x)$\\\\\\So Using $\bf{A.M\geq G.M\;,}$ We get \\\\\\$\frac{3\sin x+4-3\sin x}{2}\geq \sqrt{3\sin x\cdot (4-3\sin x)}$\\\\\\So $3\sin x\cdot (4-3\sin x)\leq 4$ and equality hold when $\sin x= \frac{2}{3}$
mycroft holmes
272 Points
7 years ago
4 – (3 sin x -2)2 
 
This is using the theory of quadratic equations without using derivatives

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