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Max, min, inflection pts

If f(x) = x^4 - 4x^3 + 10 find the relative extrema of the function and the points of inflection of its graph. Also, sketch the graph of the function. a. The x-value(s) of the relative minima of function f: ________________ b. The x-value(s) of the relative maxima of function f: _______________ c. The x-value(s) of poi

Gompertz Equation

2. The Gompertz equation y'(t) = y[a-b*ln(y)] is an important model for avascular tumor growth. In the avascular growth phase, tumor cells obtain nutrients directly from the surrounding tissue. (The transition from avascular to vascular growth is marked by the onset of angiogenesis, the formation of blood vessels, which are

Derivatives and Rate of Change : Calculate the rate a shadow is moving up a wall.

I need to determine how fast a shadow is moving up a wall. Given the heigth of the wall the height if the object that cast the shadow. The length of the wire the object moves on, and the height of the light that casts the shadow. I have worked out the first sections in an Excel 2000 spreadsheet but I need a push in the right di

Lagrangian multipliers

1) Who can explain me Lagrangian multipliers with drawings scheme etc... 1)I just can't imagine what is happening in space with Lagrangian multipliers. 2) I did this problem but here also I can't understand it, because I can't understand what is happening in space! could you explain it with drawings and schemes please : the

Evaluation the radius of curvature

Curvature (III) Differential Calculus Evaluate the radius of curvature at any point (x,y) for the curves : (a) xy = c2 (b) y = (1/2)a(ex/a +

Question about Limits and Derivatives

Please show me all of your work so that I can understand how to do the problems correctly. Please double check all of your answers to that you are sure everything is correct. Thanks. 1. Find the limit L. Then use the definition to prove that the limit is L. . 2. Find the limit: . 3. Calculate the derivative of .


Solve the following two equations. In each case, determine dy/dx: a.)y=xcos(2x^2) Is this right? y'=x(-sin)(2x^2)(4x) =-4x^2sin(2x^2) b.)y=xe^-x^2 Is this right? y'=-xe^-x^2+1(e^-x) =-xe^-x^2+e^-x


Category: Business > Management Subject: Management Science Details: 1. Which of the following statements are true for f(x) = x2? (Chapter 10) a. f(x) is a concave function b. f(x) </= 20 is a convex set c. f(x) >/= 5 is a convex set d. none of the above 2. Which of the following statements are true for f(x) =

Differentiation and Rate of Change Word Problems

1) Differentiate the equations a) y=8/5xsquared b) y=4cosX - 3ex 2)The formula C=60=t3/12 This equation refers to a machine in a workshop. This machine costs £C to lease each week according to the formula and t is the number of hours per week worked by the machine. The rate of increase of cost during the week is given by

Differentiation : Critical Point - Find Maximum Value

A manufacturer produces cardboard boxes that are open at the top and sealed at the base. The base is rectangular and its length is double its width. Let x denote the width in metres. the surface area of each such box is fixed to be 3 square metres. The manufacturer wishes to determine the height h and the base width x, in metres

Directional Derivative

Find the directional derivative of f(x,y) = 2x^3-y^2+xy at the point (1,2) in the direction of the vector (1,3). Be careful: That direction vector isn't a unit vector!

Using Dynamic Programming to Solve Problems

Please see the attached file for the fully formatted problem. Use Dynamic Programming to solve: 1. Min f(x-bar) = 3x21 + x22 + 2x23 s.t. Sx1 + 2x2 +x3 >= 18 DP Formulation:.... Min s.t. Stage 1: Stage 2: Stage 3:

Working with orthogonal trajectories

(a)Find the orthogonal trajectories of the family of curves defined by 2cy + x2 = c2, c>0 State the differential equation of the orthogonal family, and show your steps in obtaining a solution. (b) On the same set of "square" axes, plot at least five members of each of the given family and your family of orthogonal soluti

Partial derivative question

I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own. I think that I am somehow not taking the second order partial derivative right. The attached file has the professor

Partial derivatives

The heat transfer in a semi-infinite rod can be described by the following PARTIAL differential equation: &#8706;u/&#8706;t = (c^2)&#8706;^2u/&#8706;x^2 where t is the time, x distance from the beginning of the rod and c is the material constant. Function u(t,x) represents the temperature at the given time t and p


Prove that if f(x) = x^alpha, where alpha = 1/n for some n in N (the natural numbers), then y = f(x) is differentiable and f'(x) = alpha x^(alpha - 1). Progress I have made so far: I have managed to prove, (x^n)' = n x^(n - 1) for n in N and x in R both from the definition of differentiation involving the limit and the binomial

Maclaurin Series Hyperbolic Tangent

Given The Maclaurin series for the inverse hyperbolic tangent is of the form x+x^3/3+x^5/5...x^7/7. Show that this is true through the third derivative term.

Calculate the derivatives of wave equations

The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t) To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t. a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of

Definition of derivative

Let f(x) be a continuous function of one variable. a) Give the definition of the derivative. b) Use this definition to find the derivative of f(x)=x^2+2x-5 c) Evaluate f'(2)

Proof Regarding a Twice Differentiable Function

Context: We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation. Question: Let f: [a,b] --> R, a < b, twice differentiable with the second derivative continuous such that f(a)=f(b)=0. Denote M = sup |f "(x)| where x is in [a,b]

Using related rates to answer a pulley question.

Two carts A and B are connected by a rope 39 feet long that passes over pulley P. The point Q is on the floor directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 2 ft/sec. How fast is cart B moving toward Q at the instant cart A is 5 feet from Q? Express solution using related rate n

Limits and derivatives

Find the derivative. a) f= 4-sqrt(x+3) b) f= (x+1)/(2-x) See attachment below for additional information.