A plane starts its descent from height … at … to land…

A plane starts its descent from height $y=h$ at $x=-L$ to land at $(0,0)$. Choose $a,b,c,d$ so its landing path $y=a{x}^3+b{x}^2+cx+d$ is smooth. With $dx/dt=V=$constant, find $dy/dt$ and $d^{2}y/d{t}^2$ at $x=0$ and $x=-L$. (To keep $d^{2}y/d{t}^2$ small, a coast-to-coast plane starts down $L>100$ miles from the airport.)

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.5 The Product and Quotient and Power Rules, #45