I ran into this problem in the middle of my physics homework:
Using calculus, you can find a function’s maximum or minimum by differentiating and setting the result to zero. Do this for equation y = (u^2 / g)*sin(2x), differentiating with respect to x, and thus find the maximum range for x.
u = initial velocity
g= acceleration of gravity
x = theta
Possibly x = ut for range?
The Attempt at a Solution
It's been a several months since I've done this type of problem, but I tried to differentiate it through the quotient rule (and product rule) and got:
(2*g*u^2*cos(2x) + 2*g*u*sin(2x) - u^2*sin(2x)) / g^2
I tried to set this to zero in order to find the maximum:
0 = (2*g*u^2*cos(2x) + 2*g*u*sin(2x) - u^2*sin(2x)) / g^2
but I couldn't figure out what to do and I had a suspicion I was doing everything wrong.
Can anyone point out my mistakes / what to do next?