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- Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints: y = 2x2 + 4x + 5, [0, 2]find the critical points and and absolute extrema of the function y=9-x^2 on the interval [-3,1]What are the critical values & local max/min of the equation f(x)=4(x-6)2/3+2
- find the minimum and maximum value of the function on. the given interval by comparing values at the critical points and endpoints. y = x3 − 6x2 + 8, [1, 6]Market research for a certain ice cream company indicates that if the price per cup of ice cream is $50.00, the demand will be 1200 cups, whereas if the price is increased to $60.00, the demand will be 1100 cups. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (A) Find the value(s) of x at the break-even points. (B) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.Find the x coordinates of all critical points of the given function. Determine whether each critical point is relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x)=2x^3-6x+7 x=____(smaller value) x=____(larger value) 
- A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…find the minimum and maximum value of the function on. the given interval by comparing values at the critical points and endpoints. y = (2 + x) 2 + (2 − x)2, [0, 2]