Question

A ball is thrown in the air.its height at any time t is given by h=3+14t-5t^2.find the height using derivatives

Answer 1

Using derivatives we can find the slope of that function:

d/dth = 0 + 14 − 5(2t) 
= 14 − 10t

Now, find when the slope is zero:-

14 − 10t = 0

10t = 14

t = 14 / 10 = 1.4

The slope is zero at t = 1.4 seconds

And the height at that time is:

h = 3 + 14×1.4 − 5×1.42

h = 3 + 19.6 − 9.8 = 12.8

And so:-

✔The maximum height is 12.8 m (at t = 1.4 s)