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- Convexity & Concavity Consider the function defined by the formula This function is 200 if 0 < x < 20 x y = f(x) = 30- x if 20 ≤x≤40 200 if 40 < x < 60 x a. Concave but not strictly concave b. Strictly convex c. Strictly concave d. Convex but not strictly convex e. I cannot tell because the second derivative of f(x) cannot be calculatedFor what value(s) of x is the function f(x) NOT continuous? A x = 0 and x = 3 C. x = -3 only Select one: = 4 2x² — 6x B. x = 3 only D. x = 3 and x = 4Construct a table from the data shown on the graph below. Which is the dependent variable and which the independent variable? Summarize the data in equation form.
- Construct a table from the data shown. Which is the dependent variable and which is the independent variable? Summarize the data in equation form.Consider the linear spline function f(x) = 1 + x + h1(x, 2) where h1(x,2) = x-2 if x>2 and 0 otherwise. What is the slope of f at the point x=-1?If A is the dependent variable and B is the independent variable, then a change in A results in a change in B. 1) True 2) False
- Please find the effect of Y and r if there is a decrease in the tax rate. Use the following equations and evaluate the total derivative.A street vendor constructs the table below on the basis of sales data. (Note: Consumer expenditure and revenue are terms for the same thing from different perspectives. Consumer expenditure is the amount of money that consumers spend on a product, and revenue is the amount of money that businesses take in by selling the product.) Sales of Roses, Given the Price per Dozen Sales (dozen roses) Price (dollars) 20 25 30 32 (a) Find a quadratic function for the model of the data that gives the quantity sold at x dollars, data from 20 sxs 32. (Round all numerical values to three decimal places.) S(x) = 169 159 134 94 (b) Find a function for the model for consumer expenditure (revenue for the vendor), where x is the price in dollars, data from 20 sxs 32. (Round all numerical values to three decimal places.) R(x)= Need Help? (c) What price should the street vendor charge to maximize consumer expenditure? (Round your answer to two decimal places.) (d) If each dozen roses costs the vendor $11,…6). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).
- Assuming that each of the following functions are linear, give an economic interpretation of the slope of the function: a. F(q) is the revenue from producing q units of output b. G(x) is the cost of purchasing x units of some commodity c. H(p) is the amount of commodity demanded by households when its price is p d. C(Y) is the national consumption when national income is Y e. S(Y) is the total national savings when national income is Yquestion: Please find the effect of Y and r if there is an increase in the tax rate. Use the following equations and evaluate the total derivative.-2 f(x) is not continuous at x=-1, because: Select one: a. f(-1) does not exist. b. it's not a function. c. limit does not exist. d. limit from left does not exist.