Question

A model rocket is launched from the top of a building. The height (in meters) of the rocket above the grown is given by h(t)=-6t^2+30t+10 , where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height?

Answer 1

Answer:

47.5 Meters

Step-by-step explanation:

Find where the derivative changes from positive to negative (local maximum)

h(t)=$-6t^2+30t+10$

h'(t)=$-12t+30$

Find where the derivative equals zero

Theres no spot where the derivative wont exist because its a polynomial.

-12t=-30

t=$\frac{5}{2}$

Ill stop here because this is a parabola opening down and this is the only spot where there will be a horizontal tangent line so this is the x-coordinate of the vertex. AKA you don't need to test positive and negative on both sides.

Now plug into original equation

h(2.5)=$-6(2.5)^2+30(2.5)+10$

=-37.5+75+10

=47.5