Question 618720
The minus in front of the x-squared term tells me
there is a maximum and not a minimum
The maximum is halfway between the 2 roots
{{{ -16t^2 + 125t = 0 }}}
{{{ t*( -16t + 125 ) = 0 }}}
{{{ -16t = -125 }}}
{{{ t = 125/16 }}}
{{{ t = 7.8125 }}}
One root is at {{{ t = 0 }}} also, so the
halfway point is {{{ ( 7.8125 + 0 ) / 2 = 3.90625 }}}
This is the value of {{{ t }}}
The value of the function is:
{{{ f(t) = -16*(3.90625)^2 + 125*3.90625 }}}
{{{ f(t) = - 244.141 + 488.282 }}}
{{{ f(t) = 244.141 }}}
The maximum is at ( 3.907, 244.141 ) approximately