Mathematical Process Standards>Using a Problem-Solving Model to Solve and Justify Solutions(TEKS.P.9-12.1.B) Practice Test

Differentiate $E(t)$ to find when it changes slowest, set $\alpha$ equal to that slope-minimizing time's elevation, and conclude optimality without checking the power function.

Use symmetry: note $E(t)$ is even about $t=6$, so $|E(t)-\alpha|$ has its average minimized when $\alpha=E(6)$; since $\cos$ on $[0,90^\circ]$ is decreasing and even, maximizing average $\cos(|E(t)-\alpha|)$ corresponds to minimizing the average deviation; set $\alpha=E(6)$ and validate by sampling $t=3,6,9$ to compare average power against nearby tilts.

Prioritize endpoints: compute $\alpha=\tfrac{E(3)+E(9)}{2}$ so the endpoints balance, then assume this also maximizes the average without further justification.

Maximize the instantaneous peak: find the time of largest $E(t)$, set $\alpha$ equal to that value, and accept the result without analyzing the interval or checking averages.