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Math Help - How to find the maximum of a function that has 4 variables?

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    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.

    ------------------------------------------------------------------------------
    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" ?
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  2. #2
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    Quote Originally Posted by vince086 View Post
    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, \theta , as a constant ...

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

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