Exam 12: Differentiation

Suppose a person learns y items in x hours,as given by y = 50 .Find .

An object moves along the ground according to the equation x = .Find .

If y = x ,then =

The sales s of a product vary with the number of weeks of an advertising campaign according to Use the power rule to find .

Find the rate of change of y with respect to x when y = 7 - 3x + 11 .

Suppose that the profit p made by selling a certain product at a price x is given by p = f(x)and the rate of change of that profit with respect to change in price is = 6 at x = 6.Estimate the change in the profit p if the price changes from 6 to 6.5.

If an object moves horizontally according to x = 2t + 1 and vertically according to y = 2 ,find its vertical speed, .

Let p = 225 - be the demand function for a manufacturer's product.Find the rate of change of price p per unit with respect to quantity q.How fast is the price changing with respect to q when q = 10? Assume that p is in dollars.

Find y' if y = .

If y = + x,then =

Find the derivative of y = .

Find the slope of the curve y = at the point (4,13).

Find the slope of the curve y = 4 - 2x + 1 at the point (3,31).

Differentiate: h(x)= (4x - 5)

Suppose that the demand for x number of hats (in thousands)is determined by the price p of the hats as follows: x = 10 + .Find without using the quotient rule.

If the velocity function is given by V(x)= 6 + 13,find an equation of the tangent line to the graph of V(x)at (3,67).

By direct use of the definition of derivative,find (f(x))if f(x)= .

Let f(x)= - 3x + 1. (a)Find (x). (b)Evaluate (1). (c)Find an equation of the tangent line to the graph of y = f(x)at the point (1,2).

Suppose that m employees of a company produce a total of q units of a product per day,where and that the demand equation for the product is p = .Find the marginal revenue product when m = 10.

By direct use of the definition of a derivative,find if f(x)= 4x - 3.