Find the relative extrema of the function, if they exist. List each extremum alo

Question

Find the relative extrema of the function, if they exist. List each extremum along with the x-value at which it occurs. Then sketch a graph of the function. G(x) = -8x/x2 + 1 Identify all the relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The relative minima are .(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) There is no relative minimum. Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The relative maxima are .(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) There is no relative maximum. Choose the correct graph below. The total-cost, C(x), and total-revenue, R(x), functions for producing x items are shown below, where 0 le x le 700. C(x) = 4400 + 600x and R(x) = -1/2x2 + 1100x Find the total-profit function P(x). Find the number of items, x, for which the total profit is maximum. P(x) = The profit is maximized for a production of units. Determine the horizontal asymptote of the function. f(x) = 6x4 - 5x2/8x3 + 7x2 Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal asymptote. Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. f(x) = 18x2 - 3/2x3; [0,12] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The absolute minimum value is at x = and the absolute maximum value is at x = . (Use a comma to separate answers as needed.) The absolute minimum value is at x = and there is no absolute maximum. (Use a comma to separate answers as needed.) The absolute maximum value is at x = and there is no absolute minimum. (Use a comma to separate answers as needed.) There is no absolute minimum and there is no absolute maximum.

Explanation / Answer

1. relative minima is -4 at x=-1

relative maxima is 4 at x=1

graph = option (c)

2. since function value at x= inf is not converges to a fixed number. hence ther is no horizontal assymptote.

3. absolute minima = 0 at x= 0

absolute maxima = 384 at x= 8

4. P(x) = R(x)- C(x)

P(x) =-x2 /2 +500x-4400

no. of items at which profit is maximum = 500

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