The height (in meters) at time t (in hours) of a balloon in the air is given by the formula h(t)= -20t^4 + 80t + 10.

Question

A) What is the balloon's height when it starts moving?

B) What is the balloon's velocity after a half hour?

C) Find the maximum height of the balloon.

My calculus test is tomorrow, please help!!

Answer 1

h(t) = -20t⁴ + 80t + 10

A). h(0) = 10 meters

B). h'(t) = -80t³ + 80

h'(0.5) = 70 m/hr

C). At the maximum height, h'(t) = 0

h'(t) = 0 when t = 1 hour

When 0<t<1, h'(t) > 0. So, h(t) is increasing

When t > 1, h'(t) < 0. So, h(t) is decreasing

So, maximum height when t = 1.

Maximum height = h(1) = 70 meters