Exam 12: Differentiation

The reaction R to the injection of a drug is a function of the dosage x according to the equation Find the value of the derivative of this function when x = 10.

If the cost C of removing p percent of the impurities from the waste water in a manufacturing process is given by C(p)= ,find C'(p).

If the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by C(p)= ,find C'(p).

Find y' if y = .

Find the equation of the tangent line to the graph of the curve at the point (1,10).

The concentration of salt in a solution is given by C(t)= .Find the rate of change of the concentration .

Find the derivative of y = .

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 = 10 at x = 7.Estimate the change in the profit p if the price changes from 7.5 to 8.5.

Differentiate: g(x)= (x - 8)(2x - 7)(x + 5)

If the output function is given by Q(x)= + 1,find the slope of the curve at the point where x = 4.

Differentiate: g(x)= (5 - 7x + 3)(7 - 4x + 1)

Find the slope of the curve y = 3 - x at the point (2,10).

For a certain group of births,the number of people that survive to age x years is given by Find the rate of change of With respect to x when x = 26.

If f(x)= ,then (x)=

If u = (w + 1) ,find the rate of change of u with respect to w when w = 3.

Find the rate of change of y = with respect to x when x = 2.

If the output function is given by Q(x)= 5x + 122,find the slope of the curve at the point where x = 7.

Suppose the demand function for a manufacturer's product is given by p = ,where p represents the price per unit for q units.Find the marginal revenue when q = 10.

If the revenue function is given by R(x)= 6x + 4,find the derivative of the revenue function (this is called the marginal revenue).

If y = ,then find the rate of change of y with respect to x.