Question 629186
{{{ s(t) = -16t^2 + 200t + 60 }}}
Find {{{ t }}} when {{{ s(t) }}} is a maximum
The maximum ( or minimum ) of a 2nd degree
equation of the form
{{{ f(x) = ax^2 + b*x + c }}} occurs at {{{ x[max] = -b/(2a) }}}
{{{ a = -16 }}}
{{{ b = 200 }}}
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{{{ t[max] = -200/(-32) }}}
{{{ t[max] = 6.25 }}}
At {{{ t = 6.25 }}} sec, the height is a maximum
Here's a plot
{{{ graph( 400, 400, -10, 20, -30, 700, -16x^2 + 200x + 60 ) }}}