Exam 13: Additional Differentiation Topics

Find an equation of the tangent line to the curve + y + = 13 at the point (-1,3).

If y = ,use logarithmic differentiation to find y'.

Suppose the demand equation for the manufacturer's product is p = 100 ,where p is the price per unit for q units.Find the marginal revenue function.

The location of an Earth-orbiting satellite in a grid centered at the center of the Earth is given by Find .

If y = (7x + ,then find y'''.

If y = f(x)= ,find the (a)relative and (b)percentage rate of change of y when x = 0.5.

Find y' if y = .

Use logarithmic differentiation to find from y = .

If + + x = 2,use implicit differentiation to find and simplify your answer.Note: should not appear in your final answer.

The percentage p of a certain radioactive element present after t years is given by p = .Find .

Find all of the higher-order derivatives of x(t)= - - 4x.Use your graphing calculator to graph x(t)and x'(t)on the same axes.Verify that when x(t)is increasing (sloping upward),the value of x'(t)is positive.Repeat this for x'(t)and x''(t)and for x''(t)and x'''(t).

If y = ( + 5x - 1) ,then y' =

The demand function for a manufacturer's product is given by p = ,where p is the price per unit when q units are demanded. (a)Find the point elasticity of demand when q = 100. (b)For q = 100,is demand elastic,inelastic,or does it have unit elasticity?

An approximation of one root of - 3x + 1 = 0 is = 2)Apply Newton's method twice to find the approximation )

Suppose that a company can produce 15,000 units when the number of hours of skilled labor y and unskilled labor x satisfy 500 = (x + (y + .Find ,the rate of change of skilled labor hours with respect to unskilled labor hours.

Find y' if y = .

Suppose a population is growing according to the equation P = .Find the rate of growth of the population, .

If 7 + 4 = 1,then =

The total cost for a product is given by C(x)= 900 + 8 ln(3x + 7).Find the rate of change of C''(x).

The altitude (in feet)of a rocket t seconds into flight is given by h = -2 + 114 + 480t + 1,t ≥ 0.Use Newton's method to approximate when the rocket will hit the ground.