Determine where the function f(x)=³+301² is concave up and concave down, and identify all inflection points. 2. [(3 POINTS] Find lim 2-0 <- 4x 3. [3 POINTS EACH] Consider the price demand function 3z +p=400 If we solve this equation for p we get p= 400-3x. (a) Find the revenue function R(z) for this product. (b) Find the marginal revenue function for this product. (c) Determine the amount of goods z that should be produced to maximize revenue using calculus. Show your work for full credit. 4. [3 POINTS EACH] Consider the price demand function 3z+p=400 400-P 3 If we solve this equation for z we get z = (a) Find the elasticity of demand E(p) for this product. (b) Find the price p that maximizes revenue for this product using elasticity of demand. (c) Explain how your answer to this question relates to your answer to the previous question. 5. Consider the equation zy+z³y²-56 (a) [4 POINTS) Use implicit differentiation to find (b) (2 POINTS) Verify algebraically that the point (-2,4) is a solution to the equa- tion. (c) (2 POINTS] Find the value of dy dz at the point (-2,4). (d) [2 POINTS EXTRA CREDIT] Explain using calculus why this function has no local extrema (you can verify this is true by entering the equation into Desmos, but for extra credit your explanation must depend on algebra and calculus).