### Differentiation and radius of curvature

See attached for formulas

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See attached for formulas

See attached. In this question, p denotes dy/dx. Given that y=p^2+xp, show by differentiating with respect to x that dx/dp=-2-2x/p....

Find the partial derivative. [See the Attached Question File.]

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

1.) Differentiate these functions. a.) (sqrt(x)+1)/(x^2) b.) 3^x (cubedroot of (x+5)) - ((ln(x))/sqrt(x)) ----------- 2.) Consider the function f(x)= x^3- (1/2)x^2 - 4x + 5 a.) find all critical points of 'f '. b.) Does 'f ' have an inflection point? Explain your answer. c.) Determine the intervals on which 'f '

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

Please check the following derivative and explain how setting it equal to 0 you can get the value for r.

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

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

Consider the function f(x,y,z)= e^xy cos(x+z). What is the directional derivative for f at the point P(0, -pie/6, pie/3) in the direction u parallel to i - j + 2k

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 - Problems on product rule, chain rule, application type. Please see the attached file.

Questions are in the attached file.

The complete question is in the attached file.

Suppose C(r) is the total cost of paying off a car loan borrowed at an annual rate or r%. What are the units of C'(r)?

Please see the attached file for full problem description. 1. Does the graph of a function have a horizontal asymptote? If the answer is positive, find the equation of the asymptote 2. Find , when 3. Find the derivative of 4. Find the derivative of using the definition of the derivative 5. Find the antide

See the attached file. Find the derivative of the function. Find the derivative of the function. f(x) = (2 - e-6x)9 Find the derivative of the function. f(s) = (s9 + 1)e-s9 Find the derivative of the function.

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

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

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.

Please see the file attached.

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

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...

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

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 in attachment) a.) Use the date from the table to find an approximation for W'(12). Show the computations that lead to your

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

2. 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 ,

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

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

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