QuestionA model helicopter takes off from a point $O$ at time $t=0 \mathrm{~s}$ and moves vertically so that its height $y \mathrm{~cm}$, above $O$ after time $t$ seconds is given by $$y=\frac{1}{4} t^{4}-26 t^{2}+96 t, \quad 0 \leq t \leq 4$$ a) Find (i) $\frac{d y}{d t}$ (ii) $\frac{d^{2} y}{d t^{2}}$ b) Verify that $y$ has a stationary value when $t=2$ and determine whether this stationary value is a maximum or a minimum value. c) Find the rate of change of $y$ with respect to $t$ when $t=1$. d) Determine whether the height of the helicopter is increasing or decreasing at the instant when $t=3$.