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Derivatives

Cowling's rule

Cowling rule is another method for determining the dosage of a drug to prescribed to a child. For this rule, the formula d=D(a+1) ------ 24 gives the child's dosage d, Where D is the adult dosage and a is the age of the child in years. If the adult dosage of a drug is 600 milligrams and a doctor uses this formula to

Applications of the Derivative

Please see the attached file for the fully formatted problems. For the function y= sq root (x2 - 9) (i) Find the slope of the tangent line to the function at the point (5, 4). (ii) Find the equation of the normal line at the point (5, 4). 2. A ladder 10 m long rests on horizontal ground and leans against a vertical wal

Market Share Analysis

This table presents units sold and market share data for the Personal Computers Industry (first figure for each company is units, second is revenue). E-Top--10,000--7,500,000 CompEZ--15,000--12,000,000 BEST--2,000--1,700,000 Moonwalk--8,000--8,000,000 CompBrain--8,000--12,000,000 Market Total--43,000 units--41,200,000

first derivative and second derivative

Please see the attached file (word problems, inflection, critical points, and derivatives) 14. You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price wil

Application of Derivatives of Function

(See full description in the attachment). 1. With a yearly rate of 3 percent, prices are described as P = P0 (1.03)^t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15? 2. The value of a car is falling 10 percent per year so that if C0 is the purchase p

Managerial Finance - Ratio Analysis for Walmart and Target

Hello, Please assist me with the following study for my exam. Evaluate each firm's financial performance for the two most recent years available by (1) performing financial ratio analysis using the Microsoft® Excel® Ratio Analysis Worksheet, (2) performing trend analysis on those financial ratios. Your analysis should in

Rules of exponential function

Please see the attached file for full description. Post a response to the following: Explain three rules for exponents listed in the chart on p.239 (section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0). Create an expression for your classmates to solve that uses scientific notation a

Equations for modeling

1. Given the function M(t) = 2t3 - 3t2 - 36t, find the critical values and determine, using both the second derivative test and a sign chart, the nature of these values. 2. A projectile is launched with a velocity of 22 m/s at 50° to the ground. Determine its horizontal and vertical velocities. 3. Two trains start from th

Find the Max and Min. values attained by the function

I need the following problems worked out in Microsoft Word with equation editor. See the attached file. Thank you, Problem 1- Fig. 1.1 Find the Max and Min. values attained by the function (fig 1.1) on the interval [0,2] Problem 2- Fig. 2.1 A mass of clay with a volume (fig. 8.1) is formed into two cubes. W

Velocity and acceleration

The graph of the velocity v(t), in ft/sec, of a car traveling on a straight road, for 0 is greater than or equal to t is greater than or equal to 50, is shown in the attachment. A table of values for v(t), at 5 second intervals of time t, is also in the attachment. a.) During what intervals of time is the acceleration of the

With a yearly rate of 3 percent, prices are described as

1)With a yearly rate of 3 percent, prices are described as P = P0 (1.03)t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15? 2)The value of a car is falling 10 percent per year so that if C0 is the purchase price of the car in dollars, its value after t

Derivatives - Product, Chain Rules, Application type

Differentiate the following problems. Assume A, B and C are constant. Show all work. f(x)=2ex+x2 P=3t3+2et y=5*2x-5x+4 P(t)=12.41(0.94)t y=10x+10/x y=t2 + 5 ln t y=x2 + 4x - 3 ln x Solve the following problem and show work For the cost of function C = 1000 + 300 ln q (in dollars) find the cost and the

Derivatives: Temperature of a Reaction

The temperature of a chemical reaction is given by the formula: T(t) = 8e-0.3(t-2)^2 + 7, where T is the temperature and t is the time in seconds since the reaction was started. a) Draw a neat graph showing the reaction temperature during the first eight seconds of the reaction. b) What is the maximum temperature reached dur

Functions, derivatives, and critical numbers

Please show me how to reach correct solutions. Please see the attached file. Thanks in advance, Find f(x), given that... Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing. Find the critical numbers...

Derivatives and Rate of Change of Temperature

The temperature, in degrees Celsius, of the water in a pond is a differentiable function W of time t. The table below shows the water temperature as recorded every 3 days over a 15-day period. (Chart is in attachment) a) Use the date from the table to find an approximation for W'(12). Show the computations that lead to you

Derivatives and Maximum Profit

3. Parcel Post A firm wishes to use the services of a parcel delivery company to transport a cylindrical package. The package has volume V=pr2l, where l is the length of the package in metres and r is the radius of the circular end in metres. The parcel delivery company will only transport parcels provided that the sum of the

Derivatives: Determining Maximum and Minimum Values

1). An open rectangular box with square ends is to hold 6400 cm^3. It is built at a cost of $ 75/ cm^2 for the base and $25/ cm ^2 for the sides. Find the most economical dimensions. 2). A wall 8 meter high is 3 3/8 meter from a house. Find the shortest ladder which will reach from the ground to the house when leaning over t

Derivatives : Maximum and Minimum Values

5). The total cost of producing x radio sets per day is $ ( 1/4 x^2 + 35x + 25 ) and the price per set is at which they may be sold is $ ( 50 - 1/2x ). Find the daily output for maximum profit. Answer 10 sets /day 6). The cost of fuel in running a locomotive is proportional to the square of the speed and is $25/hr for a

Maximizing and Minimizing using Derivatives

2) A piece of paper for a poster contains 1000 cm^2. The margins at the top and bottom are 9cm and the side margins are 6 cm. What are the dimensions of the sheet if the printed area is to be a maximum. Answers 2root3 and 3root3 3) At 9am ship B was 65km due east of ship A. Ship B was then sailing west at 10km/h and A was s

Optimization using Derivatives: Example Problems

a) A man in rowboat at point P, 150km from the shore, wishes to reach a point B, 600 km down shore, in the shortest amount of time. Where should he land if he can row at 4km/hr and walk at 7km/hr? b) If high school prom tickets cost $16 then 1000 people will attend the dance. For every $1 increase in the price 30 fewer people

Derivatives and Rate of Change

A vat with 600 gallons of beer contains 4% alcohol (by >volume). Beer with 6% alcohol is pumped into the vat at a rate of 6 gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour? (Round the answer to one decimal place.) p(60) =

Wave Equations and Energy Density

For a solution of the wave equation with p=T=C=1 the energy density is defined as e=1/2 (U_t ^2 + U_x ^2) and the momentum density as p=U_t*U_x Show that de/dt=dp/dx and dp/dt=de/dx Show that both e(x,t) and p(x,t) also satisfy the wave equation http://tosio.math.toronto.edu/pdewiki/index.php/2006APM346Midterm1 It's

Slope predictor function, derivative, maximization

Given f( x) = 2/x-1 , use the four step process to find a slope predictor function m(x). Then write an equation for the line tangent to the curve at the point x = 0. Find f'(x) given f (x) = 5x^3- 4x^2+ 3x- 2 / X^2 . A farmer has 480 meters of fencing. He wishes to enclose a rectangular plot of land and to divide

Derivatives and tangents

Use the definition of the derivative to find f '(x) given f(x)=^/¯x Write an equation of the line tangent to the curve at the point P(-1, 7). Express the answer in the form ax + by = c. y= 5/x^2-2/x^3 Write the equation of the line tangent to the curve at the point P where x = 4. Write the equation in the f

minimizing the average cost

A domestic auto producer is facing intense competition in the US market from Asian imports. The CFO decides that the solution is to produce at the point at which average cost is minimized, i.e. where TC/Q is at a minimum. The firm's cost structure is given by: TC={(1/3Q)^3}-{(100Q)^2}+20,000Q Calculate the average cost-min

Find the partial derivatives ..

Please see attachment. 4.10 Find the partial derivatives with respect to x, y, and z of the following functions: (a) f(x,y,z) = ax^2 +bxy + cy^2 (b) g(x,y,z) = sin(axyz^2), (c) h(x,y, z) = ax^(xy/z^2). where a, b, and c are constants

L'Hospital's Rule

Please see the attached file for the fully formatted problems. 17 L`Hospital`s Rule These are instructions from my professor he wants us to use this form & these rules to do the problems. He wants us to follow these sepd. Please help, I appreciate it. There are 3 problems in this set and 3 pages. thx Note this is not the Q

Solve: Decreasing Functions

Determine the intervals on which the function is increasing and intervals on which the function is decreasing. Check your answers by graphing the corresponding functions. - Please view the attachment for the rest of the solution. Question: Determine the intervals on which the function is increasing and intervals on whic