Question

The path of an object is given by the function s=-(1/2)t^2+3t+5, where t is the time in seconds and s is the height of the object in feet. The maximum height of the object is ___ feet.

Answer 1

Set the derivative of \[\frac{1}{2} \left(-t^2+6 t+10\right) \]to zero and solve for t.
Verify that t=3.
A plot is attached.