Question

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

Answer 1

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)`