The function $H(t)=-4\mathrm{.}9t^{2}20\mathrm{.}1t1\mathrm{.}6$ takes $t,$ seconds since an object is thrown into the air, and gives $H,$ how high the object is above the ground $($in meters$).$

Answer the following three questions:

a$)$ Determine the derivative ${}^{\text{'}}(t)$

b$)$ Solve for when $H(t)=3$ or state there are no solutions $($Please note this is the original $H(t),$ not $H^{\text{'}}(t))$ Include proper units with your answer$($s$).$

c$)$ Determine the value of $H^{\text{'}}(3)$ or state there are no solutions. Include proper units with your answer$($s$).$

$2$ points for the correct derivative in part a$)$

$1$ point for number value$($s$)$ of part b$)$

$1$ point for units of part b$)$

$1$ point for number value$($s$)$ of part c$)$

$1$ point for units of part c$)$

$($olease note this means there are four possible extra credit points$)$