Due on November 30th. Bring a physical copy of the HW to class on that day. PS: 10 extra points will be given for writing the HW in LateX. I recommend using authorea.com as it is the most intuitive software of its kind.

1 Write the rules for differentiation for linear, power, exponential, and logarithmic functions

2 Write the formula for the product rule and the quotient rule of differentiation

3 Write the proof for the product rule

4 Write the formula for the chain rule

5 Write the proof for the chain rule

6 What is the formula for price elasticity of demand? What the one for the income elasticity of demand? Finally, what is the cross price elasticity of demand?

Use the following notation for the demand function
\(D: Q(P)\)

7 What is "Polonius' point"? Set up the intertemporal utility maximization problem for an individual over two periods (i.e., \(t=1,\ 2\)). Find the formula for consumption in the first period as a function of the interest rate, the discount rate, and income over the two periods.

8 What is l'Hopital's Rule? Use the rule to find the following limit: \(\lim_{x\to 0}\frac{e^{x}-1}{x}\)

9 Define convex, concave, strictly convex, and strictly concave curves using the notion of derivative (hint: not just first derivative!)