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# Derivatives

### Partial derivatives

Find the indicated partial derivative. Please see the attached file.

### Second partial derivatives

Find all the second partial derivatives. Please see the attached file.

### Sequences and derivatives

Please see the attached file. Determine whether the sequences....converges or diverges.....

### Show that if (x/y)^1/2 + (y/x)^1/2 = 10, then dy/dx = y/x

Show that if (x/y)^1/2 + (y/x)^1/2 = 10, then dy/dx = y/x

### Derivatives and Relations Functions

Show that for the relation (xy)^12 + (y/x)^1/2 = 10, x and y cannot = 0, dydx = yx

### Forward Difference, Central Difference and Extrapolation

The attached Word document contains all three requested solutions. The problems employ Forward Difference and Central Difference formulas to estimate f'(x) and f''(x). Please see the attached file for the fully formatted problems.

### Functions and derivatives

Please help me with steps. Please see the attached file. Thanks in advance 1. Does there exist a differentiable function f so that f(-3) = -2, f(1) = -6, and f ' (x) > 0 for all x? 2. Find all numbers c in the interval (1,2) that satisfy the conclusion of the mean-value theorem. 3. Give the values of x for which the

### 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...

### Traveling Wave Verify Equation

See attached file. Verify that (6-85a) and (6-85b) are solutions to (6-84a). 6-84a: The partial derivative has been replaced by the ordinary derivative since is only a function of the radial coordinate. The differential equation 6-84a has two independent solutions 6-85a: 6-85b: Equation 6-85a represent

### 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 and Maximum Profit: Example Problem

DVD Player Company A DVD player company's weekly production costs, denoted by C, is given by the expression: C=4x2+10x+30 Where x is the selling price of DVD players produced, in pounds. The number of DVD players sold each week is given by S= 400 -x and the weekly revenue is given by R = Sx. The weekly profit, P, can be

### Differentiation of a Moment Generating Function

M'(t) = (μ+tσ²) exp {½ t²σ² + μt} m'(t) = (μ+tσ²) exp {½ t²σ² + μt} + σ²exp {½ t²σ² + μt} m''(t) = ?? Please help

### Vectors, Gradients and Directional Derivatives

Find the directional derivative of f at the given point P in the direction indicated by the angle theta. f(x,y)= (x^2 - y)^3 P(3,1) theta= 3pi/4

### 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

### Finding the Directional Derivative: Example Problem

Find the directional derivative of the function at a given point P in the direction of the vector V: f(x,y,z)= square root of xyz P(2,4,2) V=(4,2,-4) and f(x,y,z)= z^3 - (x^2)(y) P(1,6,2) V=(3,4,12)

### 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

### Derivatives and Tangent Lines

3. Answer these questions. a. Find f'(x) where f(x)= 3x4 + 2 - b. Find the equation of the tangent line at x=1 for the function f(x) from part a. c. Find for y=2lnx+5x -2log3x

### Derivatives and Extrema

For the function f(x)=(x)/(x^2+9) a) Find f'(x) using the appropriate rule and simplify to one expression with positive exponents. b) Find all values of x, using algebra, where f'(x)=0 (Write your answer with positive exponents) *** I could really use some help on this one. Thanks :)

### Avg. Rate of Change /Find Derivative /Instant Rate of Change

For the function f(x)=(3x)/(x+2) a. find the average rate of change from x=2 to x=5 b. find the derivative f'(x) from first principles, by setting up the difference quotient, (f(x+h)-f(x))/(h) and finding lim h->0 (f(x+h)-f(x))/(h) c. use part b to find the rate of change of f(x) at x=2

### Definition of the Derivative

Specifically, I want you to calculate each derivative using our limit formula: and 1. f(x) = 7 2. 3. 4. 5. 6. Assume and . Calculate the derivative of [ ].

### Mean Value Theorem: Roots of Derivatives on an Interval

The function f (x) and all of its derivatives are continuous on [0, 10]. You know that f (0) = 0, f (2) = 0, f (3) = 0, f (6) = 0, and f (8) = 0. At how many points must the first derivative of f (x) be zero? At how many points must the second derivative of f (x) be zero? At how many points must the third derivative of f (x) b

### Derivatives and equations of motion

A ball thrown vertically upward at time t=0(s) with initial velocity 80 ft/s and initial height 96ft and height function of y(t) = -16t^2 + 80t + 96. a)what is the max height attained by the ball? b) When and with what impact speed does the ball hit the ground?

### 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

### Directional Derivatives

Find the derivative of the function f=xy^2 + xz at the point (1,1,2) in the direction of the vector : U = 2*i - j + 2*k where i, j, k are the unit vectors.

### Differentiate the function f(x) (a) xlnx - x (b) x^5 lnx (c) (lnx)^2 (d) (1-x) / lnx (e) 1- x / lnx

Differentiate the function f(x) = (a) xlnx - x (b) x^5 lnx (c) (lnx)^2 (d) (1-x) / lnx (e) 1- x / lnx