1) Let f(x)=ln(3). What is f'(x) when x=1.0?
2) Assume SSE(b)=(5-1*b)^2+(5-5*b)^2 +(8-10*b)^2 . Find the value of b that will minimize this function.
3) What is the consumer surplus when the inverse demand curve is defined by P=1000-((Qd)^3) and the equilibrium quantity level is 4?
Hint 1: Calculate the area under the Demand curve from 0 to 4.
Hint 2: Calculate TR.
Hint 3: Area under- TR
4) What is the x-value associated with the inflection point of the following function: 25*x^3 +100*x^2+ 18.2*x?
Hint 1: Set second derivative equal to zero and solve.
5) Given the following objective function: U(x,y)=x^2+y^2 and the following constraint: 410=8*x+20*y, please solve for the optimal value of y.
6) Given the following objective function: f(x,y)=-3*x^2 - 1*y^2 +3*x*y+1413*x+1331*y , please identify the optimal value for x.
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