Answer: At [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.
Step-by-step explanation:
Since we have given that
Distance at which Selena is standing on a rock cliff = 52 feet
Height of boulder above a rock cliff = 12 foot
So, the given quadratic equation would be
[tex]p(t)=-16t^2+12t+52[/tex]
First we derivative it w.r.t t,
[tex]p'(t)=-32t+12[/tex]
Now, we will find the critical value,
[tex]-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}[/tex]
Now, we will check whether it is maximum or not.
[tex]p''(t)=-32<0[/tex]
So, we get that it is maximum.
Hence, at [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.
