Exam 12: Differentiation

Money is invested in an annuity that earns r percent per year,compounded monthly.The future value S of $2000 invested in such an annuity for 5 years is S = 2,000 .Find S'.

Find y' if y = .

Find if y = .

Find y' if y = ( - 10x + 2)( + 7x + 1).

If y = - and u = ,then by direct use of the chain rule find and evaluate when x = 5.

If C = 10 + 0.7I - 0.2 is a consumption function,then the marginal propensity to consume and the marginal propensity to save when I = 25 are respectively given by

If the amount of money hidden in your great-aunt's mattress is given by the equation A(t)= $643,find .

A bus company will plan a group trip for groups of 10 or larger.If the group is exactly 10,the cost is $50 per person.The company offers to discount each person's ticket by $2 for each addition to the group above 10.The revenue for the bus company is given by: R(x)= (10 + x)(50 - 2x)where x is the number of additional people above 10.Find the marginal revenue function using the product rule.

The path of a projectile is given by y = .Find an equation of the tangent to this curve at x = 1.

The demand for a product is given by the equation p = .Find the marginal demand without using the quotient rule.

Suppose you sell cups of caffe latte for $3 each.If you sell q cups of latte,the total revenue r is given by Find the marginal revenue.

Differentiate: f(x)= 4x

The demand D for a product at price x is given by D = -3 + 100.Find and discuss what happens at x = 0.

The typing speed of a certain computer student varies with the number of hours of practice x according to Find S'.

Suppose the position function of an object moving along a number line is given by s = f(t)= + 4t,where t is in seconds and s is in meters. (a)Find the average velocity over the interval . (b)Find the velocity when t = 5.

The total revenue r for selling x number of bicycles is given by r = 380x.Determine the relative and percentage rates of change of revenue with respect to x when 4 bicycles are sold.

If the output function is given by Q(x)= + 1320,find the slope of the curve at the point where x = 1.

Find y' if y =

Differentiate: f(x)= (3 + x)(8x - 7)

A particle travels along a straight line path according to the equation of motion s = where t is in seconds and s is in meters.Find the velocity of the particle at t = 4.