# How to find the maximum of a function that has 4 variables?

• Apr 2nd 2011, 11:06 AM
vince086
How to find the maximum of a function that has 4 variables?
I have this question to solve for maths, I am not interested in getting the result just like that, I want to calculate it myself so that I will know how later on by myself.

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A particle is launched with velocity v from ground level at an angle  to the horizontal. It is possible to show that its height above ground is given by the function

sy(t) = v*t*sin (r) - (1/2) g*t^2

where g is the downward acceleration due to gravity. For what value of t is sy maximized?
You should derive an expression in terms of v;  and g.
t = 
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So from what I can tell I need to derive the function in a certain way (way to go sherlock), something that I can do easily with a simple function with just one variable.

I am wondering how would I go about solving this and how do you "derive an expression in terms of v;  and g" ?
• Apr 2nd 2011, 11:49 AM
skeeter
Quote:

Originally Posted by vince086
I have this question to solve for maths, I am not interested in getting the result just like that, I want to calculate it myself so that I will know how later on by myself.

------------------------------------------------------------------------------
A particle is launched with velocity v from ground level at an angle to the horizontal. It is possible to show that its height above ground is given by the function

sy(t) = v*t*sin (r) - (1/2) g*t^2

where g is the downward acceleration due to gravity. For what value of t is sy maximized?
You should derive an expression in terms of v; and g.
t =
-------------------------------------------------------------------------------

So from what I can tell I need to derive the function in a certain way (way to go sherlock), something that I can do easily with a simple function with just one variable.

I am wondering how would I go about solving this and how do you "derive an expression in terms of v; and g" ?

treat the launch angle, $\displaystyle \theta$ , as a constant ...

$\displaystyle \dfrac{dy}{dt} = v\sin{\theta} - gt$

set $\displaystyle \frac{dy}{dt} = 0$ and solve for $\displaystyle t$ ... the time when the velocity in the y-direction is zero, indicating when the projectile is at its maximum height.