If the function is given implicitly by $xe^y -
3y \sin x = 1$, find $y'$ by implicit differentiation.

Sketch the graph of the function $f(x) = \frac{5x}{x^3 - x}$ by first finding:

(a) The domain and asymptotes.

(b) Intervals of monotonicity and concavity.

(c) Local extrema and inflection points.

(a) The domain and asymptotes.

(b) Intervals of monotonicity and concavity.

(c) Local extrema and inflection points.

3. A boat leaves the dock at 2 pm. and travels due
south at a speed of 20 km/h.
Another boat has been heading due east at 10 km/h and
reaches the dock at
3 pm. At what time were the two boats closest to each
other?

5. Find the equation of the tangent line to the
curve $e^x$ that passes through the
origin.

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