Question

The height (in meters) of an object thrown vertically into the air is given by h(t) = -5t^2 + 20t + 10, where t is the time in seconds. Determine the maximum height the object reaches and the time it takes to reach that height.​

Answer 1

Hi,

Explanation:

if i can use derivation

`h(t)=-5t^2+20t+10\\h'(t)=-10t+20\\h'(t)=0 \\\Longleftrightarrow\ -10t+20=0\\\Longleftrightarrow\ t=2\\\\\\h''(t)=-10 < 0 \Longleftrightarrow\ a\ maximum\\\\h(2)=-5*2^2+20*2+10=30\\`

the maximum height is 30 m.