Exam 12: Differentiation

Find y' if y = .

Find the slope of the curve y = at the point (3,-4).

The revenue R from the sale of x units of a product is R = + 10x.The number of units sold after t weeks of advertising is x = 7 + .Find when t = 3.

Find the slope of the curve y = at the point where x = 5.

Find y' if y = ( + 9) .

If the velocity function is given by V(x)= - 22.63,find an equation of the tangent line to the graph of V(x)at (3.51,63.6107).Use your graphing calculator to verity that the graph of V(x)and the tangent line are at the point (3.51,63.6107).

The height of a boulder just sitting on a 30-foot cliff is given by y = 32.Graph this function on your graphing calculator and describe its slope.

The path of a projectile is given by y = x + .Find an equation of the tangent to this curve at x = 2.

Find if y =

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

Find y' if y = .

The total cost (in dollars)of producing x portable radios per day is The marginal cost of producing x radios is found by taking the derivative of C(x).What is the marginal cost of producing x radios?

If y = - - 5u - 6 and u = - 2x -13,then by direct use of the chain rule find and evaluate when x = 2.

A fruit stand usually sells 85 apples per day at $0.60 each.A business student's research tells her that for every $0.05 decrease in price,the stand will sell 8 more apples per day.The revenue function for the fruit stand is given by: R(x)= (0.60 - 0.05x)(85 + 8x)where x is the number of $0.05 reductions in price.Find ,the marginal revenue.

The cost C of obtaining water that contains p percent impurities is given by C(p)= - 1200.Rewrite this function so that all terms are in the form .

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

Find the rate of change of the area of a square with respect to its one side.Evaluate it when side = 4 units.

In a predator-prey experiment,it was statistically determined that the number y of prey consumed by an individual predator was a function of prey density x (the number of prey per unit of area)where Determine the rate of change of prey consumed with respect to prey density.

Suppose the demand function for a manufacturer's product is given by p = 20 - 0.8q,where p represents the price per unit for q units.Find the marginal revenue when q = 10.

Find if y = (x + 2).