Unit 2B Practice Exam B Answer Key

Use zeros of $v=t(t-2)(t-4)$ and $a=3t^2-12t+8$.

$v(t)=8e^{-t/5}[-\frac15\cos(2t)-2\sin(2t)]$.

Relative volume error approximately $3(0.4\%)=1.2\%$.

Similarity gives $r=h/3$, so $V=\pi h^3/27$ and $dh/dt=27(dV/dt)/(3\pi h^2)$.

$R'>0$, $R"<0$, and $R\to100$.

Domain excludes $\pm1$; combine asymptotes with derivative sign charts.

With $r^2h=500$, minimum material gives $h=2r$.

Construct separate land and underwater distance functions before differentiating total cost.

Labor elasticity is $0.6$; a $1\%$ labor increase gives about $0.6\%$ output increase locally.

$1$.

$0$.

Newton iterates cycle $0\to1\to0$.

For convex $f$, tangent inequality with $f'(c)=0$ gives $f(x)\ge f(c)$.

A strong critique names one specific assumption, explains how reality may violate it, and states how the conclusion could change. For stopping distance, one may criticize the assumptions of fixed reaction time and uniform braking conditions: fatigue, wet pavement, tire wear, and slope can all increase stopping distance, so the fitted model should be recalibrated for those conditions. For the medication model, one may criticize the assumption of one uniform patient response: metabolism, body mass, kidney function, and interactions can shift both the peak time and concentration. Full credit requires the assumption, its consequence, and a proposed measurement or model improvement.