Exam 12: Differentiation

Find y' if y = .

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

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

A pizza maker sells large pizzas for $13 each.If he sells q large pizzas,the total revenue r is given by Find the marginal revenue.

Find if y = 0 - + 3.927 + 1.9x.

Find all values of x for which the curve y = + 6x - 4 has a horizontal tangent line.

Find y' if y = .

If the profit for a telephone company (in millions of dollars)is given by the equation use the derivative function on your graphing calculator to find the slope of the tangent to this curve at x = 3.69.

When a ball is thrown downward at a speed of 35 feet/s from a height of 1000 feet,its height H in feet after t seconds is given by H = 1000 - 35t - .Find .

Money is invested in an annuity that earns r percent per year,compounded monthly.The future value S of $10,000 invested in such an annuity for 6 years is S = 10,000 .Find S'.

The position of an object dropped from a height of 400 feet is given by: Find the rate of change of y with respect to t and evaluate it when t = 1 and t = 3.Interpret your results.

Find the equation of the tangent line to the graph of the curve y = at the point (3,1).

The concentration of salt in a solution is given by C(t)= .Find when t = 64.

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

Suppose a person with x years of eduction before seeking regular employment can expect to receive an average yearly income of y dollars per year,where y = + 5200,4 ≤ x ≤ 16.For what value of x is y increasing at the rate of 600 (dollars/year of education)?

The demand for a product is given by D(x)= - 1.Rewrite this function so that all terms have the form .

Find the slope of the curve y = 2 at the point (4,4).

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

Differentiate: f(x)= ( + )(2 - )

Find the rate of change of y = x( + 9x + 3)with respect to x.