Let x be the number of units produced. The company wants to know how many units

Question

Let x be the number of units produced. The company wants to know how many units to make in order to maximize profit. Remember that Profit = Revenue- Cost. At the optimal value of x, R'(x) > C'(x) True False 1 points Save Answer QUESTION 5 When the derivative is equal to 0 at a value of x O the function will be equal to 0 at that value of x the function has a critical point at that value of x the second derivative will be 0 at that value of x Each of the above is true. 1 points Save Answer QUESTION 6 In this example, f(5) = 20 and f(6)-25. In addition, f ' (5) > f ' (6) and there are no critical points between x = 5 and x = 6. What can be said about f"(5)? O It is positive It is zero O It is negative There is no way to tell from this information

Explanation / Answer

1) This statement is false because the value of revenue may not always be greater than the cost price so in that case C'(x)>R'(x) so the above statement is false.

2) When the derivative is 0 at a value of x it means f(x) is either maximum or minimum at that point means the slope of the curve is 0 at that point and the function has a critical point at that value of x

3) f(5)=20 and f(6)=25 and there are no critical points between 5 and 6 it means the curve is an increasing function as f'(5)>f'(6) means the slope of curve at x=5 is greater than the slope of curve at x=6

so the f ' ' (5) is negative because the f ' (x) is a decresing function as you can observe beacuse f'(5)>f'(6) means f'(x) is decresing as the value of x increases so f ' ' (x) will be negative.

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