1. [-/1 Points] DETAILS HARMATHAP12 9.4.001. MY NOTES Find the derivative of the function. y = 63 Need Help? Read It Watch It Submit Answer 2. [-/1 Points] DETAILS HARMATHAP12 9.4.003. MY NOTES Find the derivative of the function. f(t) = 4t f' (t ) = Need Help? Read It Submit Answer 3. [-/1 Points] DETAILS HARMATHAP12 9.4.005. MY NOTES Find the derivative of the function. y = 7 - 9x + 8x2 Need Help? Read It Submit Answer 4. [-/1 Points] DETAILS HARMATHAP12 9.4.007. MY NOTES Find the derivative of the function. f(x) = 4x4 - x6 f' ( x) = Need Help? Read It Submit Answer5. [-/1 Points] DETAILS HARMATHAP12 9.4.014.MI. MY NOTES Find the derivative of the function. h(x) = 10x16 + 4x8 - 2x5 + 19x - 5 h' ( x ) = Need Help? Read it Watch It Master It Submit Answer 6. [-/2 Points] DETAILS HARMATHAP12 9.4.015. MY NOTES For the function y = 6x2 + 3x + 4, at the point x = 4, find the following. (a) the slope of the tangent to the curve (b) the instantaneous rate of change of the function Need Help? Read It Watch It Submit Answer 7. [-/2 Points] DETAILS HARMATHAP12 9.4.017. MY NOTES For the function P(x) = x3 - 9x, at the point (3, 0), find the following. (a) the slope of the tangent to the curve b) the instantaneous rate of change of the function Need Help? Read It Submit Answer8. [-/1 Points] DETAILS HARMATHAP12 9.4.019. MY NOTES Find the derivative of the function. y = x-3+x-2 - 4 y' ( x ) = Need Help? Read it Watch It Submit Answer 9. [-/1 Points] DETAILS HARMATHAP12 9.4.025. MY NOTES Find the derivative of the function. g ( x ) = - x3 X 2 2 + 9V x g' ( x) = Need Help? Read It Watch It Submit Answer 10. [-/1 Points] DETAILS HARMATHAP12 9.4.050. MY NOTES The monthly output of a certain product is Q(x) = 2700x5/2 where x is the capital investment in millions of dollars. Find dQ/dx, which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. dQ/dx = Need Help? Read It Watch It Submit Answer11. II4 Points] DETAILS HARMATHAP1Z 9.4.051.M[. The demand for 47 units of a product depends on the price p (in dollars) according to Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is as follows. (a) $16 256 l Interpret the instantaneous rate or change. O 0000 (b) $64 a: *1,rorp>0. i/E If price decreases by $1, the demand will drop by the absolute Value of this number of Units. it price increases by $1, the demand will increase by the absolute value or this number or units. If Drlce Increases by $1, the demand will drop by the absolute value of this number of units. it price decreases by the absolute value of this amount, the demand will drop by 1 unit. it price increases by the absolute value ot this amount, the demand will drop by 1 unlt, l interpret the instantaneous rate of change, O 0000 it price decreases by $1, the demand Will drop by the absolute value ofthls number of units. If price increases by $1, the demand will increase by the absolute value or this number or units. If price increases by $1, the demand will drop by the absolute value of this number of units. it price decreases by the absolute value of this amount, the demand will drop by 1 unit it price increases by the absolute value of this amount, the demand will drop by 1 unit. Need new _E Submit Answer MY NOTES 12. [-/4 Points] DETAILS HARMATHAP12 9.4.052. MY NOTES Suppose that the demand for a product depends on the price p according to D(P) = 80,000 P > 0 p2 where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price for the following values of p. (a) p = 50 Interpret the instantaneous rate of change. O If price increases by $1, the demand will increase by the absolute value of this number of units. O If price decreases by this amount, the demand will drop approximately 1 unit. O If price increases by this amount, the demand will drop approximately 1 unit. O If price decreases by $1, the demand will drop by the absolute value of this number of units. O If price increases by $1, the demand will drop by the absolute value of this number of units. (b) p = 100 Interpret the instantaneous rate of change. O If price increases by $1, the demand will drop by the absolute value of this number of units. If price decreases by $1, the demand will drop by the absolute value of this number of units. O If price decreases by this amount, the demand will drop approximately 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units. O If price increases by this amount, the demand will drop approximately 1 unit. Need Help? Read It Submit Answer 13. [-/1 Points] DETAILS HARMATHAP12 9.9.009.MI. MY NOTES Cost is in dollars and x is the number of units. Find the marginal cost function MC for the given cost function. C(x) = 44 + 6x MC = Need Help? Read It Master It Submit Answer14. [-/1 Points] DETAILS HARMATHAP12 9.9.012. MY NOTES Cost is in dollars and x is the number of units. Find the marginal cost function MC for the given cost function. C(x) = 600 + 15x + 0.03x2 MC = Need Help? Read It Watch It Submit Answer 15. [-/1 Points] DETAILS HARMATHAP12 9.9.015. MY NOTES Cost is in dollars and x is the number of units. Find the marginal cost functions MC for the given cost function. C = 700 + 26x + 2x3 MC = Need Help? Read It Submit Answer 16. [-/3 Points] DETAILS HARMATHAP12 9.9.017. MY NOTES Suppose that the cost function for a commodity is C(x) = 60 + x2 dollars. (a) Find the marginal cost at x = 7 units. MC(7) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit. $ Need Help? Read It Watch It Submit Answer17. [-/3 Points] DETAILS HARMATHAP12 9.9.020.MI. MY NOTES If the cost function for a commodity is C(x ) = - 90 1x3 + 4x2 + 4x + 20 dollars find the marginal cost MC at x = 9 units. (Round your answer to two decimal places.) MC = $ Tell what the marginal cost predicts about the cost of producing 1 additional unit. The cost of producing 1 additional unit is $ Tell what the marginal cost predicts about the cost of producing 2 additional units. The cost of producing 2 additional units is $ Need Help? Read It Master It Submit Answer 18. [-/2 Points] DETAILS HARMATHAP12 9.9.025. MY NOTES Cost, revenue, and profit are in dollars and x is the number of units. If the total profit function is P(x) = 5x - 28, find the marginal profit MP. MP= What does this mean? O This is the total profit. O The next unit sold costs this much to make. O This is the total cost. O This is the total revenue. The next unit sold earns this much profit. Need Help? Read It Submit Answer19. [-/7 Points] DETAILS HARMATHAP12 9.9.027. MY NOTES Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function for a product is R(x) = 50x and that the total cost function is C(x) = 1800 + 30x + 0.01x2. (a) Find the profit from the production and sale of 500 units. $ (b) Find the marginal profit function. (c) Find MP at x = 500. MP = Explain what it predicts. The total profit will [---Select--- by approximately $ on the sale of the next (501st) unit. (d) Find P(501) - P(500). $ Explain what this value represents. O This is the actual profit on the sale of the 501st unit. This is the actual cost of the 501st unit. O This is the total profit for 501 units. O This is the actual revenue on the sale of the 501st unit. O This is the total cost of 501 units. Need Help? Read It Submit Answer20. [-/6 Points] DETAILS HARMATHAP12 9.9.028. MY NOTES Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by R(x) = 49x and that the total cost function is given by C(x) = 90 + 30x + 0.1x2 (a) Find P(100) P(100) = (b) Find the marginal profit function MP. MP (c) Find MP at x = 100. MP(100) = Explain what it predicts. At x = 100, MP(100) predicts that profit will decrease by |MP(100) | dollars. O At x = 100, MP(100) predicts that cost will increase by IMP(100) | dollars. O At x = 100, MP(100) predicts that cost will decrease by IMP(100) | dollars. At x = 100, MP(100) predicts that profit will increase by IMP(100) | dollars. (d) Find P(101) - P(100). $ Explain what this value represents. The sale of the 101st unit will decrease profit by [P(101) - P(100) | dollars. O The sale of the 101st unit will increase profit by [P(101) - P(100) | dollars. O The sale of the 100th unit will increase profit by [P(101) - P(100) | dollars. The sale of the 100th unit will decrease profit by [P(101) - P(100) | dollars. Need Help? Read It Watch It Submit