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Given g(x) = sin(x)cos(x) in the closed interval [0, pi/2], what is the absolute maximum value of g?

User Brujoand
by
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1 Answer

6 votes

Answer:
(√(2) )/(4)

Explanation:

Find Critical Points

Derive the original function giving you


cos(2x)

Setting this equation equal to 0 we are able to find 3 seperate solutions being

x = 0


x = (\pi )/(2)


x = (\pi )/(4)

Plugging each of these into the original function to see what is the highest number gives us


(√(2) )/(4) when
x = (\pi )/(4)

User Steve Paulo
by
8.3k points

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