Question

How do you know that 2 is the maximum value for 4sinxcosx?

Answer 1

4 sin x cos x = 2. 2 sin x cos x
= 2 sin 2x
<= 2 since maximum value for sin is always 1 (so sin 2x <=1)

Answer 2

im not sure im following what you did with the cosx

Answer 3

sin 2x = 2 sin x cos x (its an identity)

Answer 4

haha its been awhile

Answer 5

Because when sin(x) is at its max, cos(x) is 0. And vice versa for cos(x). So the bigest value you can get for their product is at \(\large x=\frac{\pi}{4}\)

Answer 6

Or yeah, if you can remember all those silly identities you can do it that way.