Need to solve a word problem.?

Question

An object is tossed into the air with an upward velocity of 14 ft/s will rise and fall according to the equation s=14t-16t^2. At what time is the object at maximum height?

Thanks

Answer 1

just explaining what the guy above me is having you do..

taking the derivative will give you velocity

finding the critical point will help you find what time the velocity is equal to zero... b/c for that split second when v=0, the object is changing its direction, thus making that its heighest point...

Answer 2

as noted, you can take the derivative, set it equal to zero, and find the maximum (where the object stops moving up and starts moving down, the rate of change is zero).

for quadratics there is a simple way to find the vertex.. if you have an equation in standard form the x value (or in this case t) of the coordinates of the vertex is -b/(2a)

(standard form is y = ax^2 + bx + c)

so for this a = -16, b = 14, (and c = 0)

so maximum height is at t = -14/[2*(-16)]

hope this is clear.

Answer 3

take the derivative and find the critical point...