### Find the relative maxima, relative minima, and saddle points of the given function of two variables.

Find the relative maxima, relative minima, and saddle points of the function (x^2)*y - 6*(y^2) - 3*(x^2).

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Find the relative maxima, relative minima, and saddle points of the function (x^2)*y - 6*(y^2) - 3*(x^2).

Use an appropriate form of the chain rule to find dz / dt for z = 3 cos x - sin x y ; x = 1/t, y = 3t .

See the attached file for full description. 40) The value of a certain automobile purchased in 1997 can be approximated by the function v(t)=25(0.85)^t , where t is the time in years, from the date of purchase, and v is the value, in thousands of dollars. (a) Evaluate and interpret v(4). (b) Find an expression for v1(t) inclu

Find the mass M (in grams) of a rod coinciding with the interval [0,4] which has the density function p(x)=5sin(pi/4)x See attached file for full problem description.

Can someone please help solve and understand this problem. The answer to the question are (a) All Values; (b) alpha = m/(m+4n). See attached file for full problem description.

A mass of clay of volume 432 in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?

1.) Integral of [(x^5 ) / (x^2+4)^2]dx

1) Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10. Determine the domain and the range of this function. 2) The wave equation (c^2 ∂^2 u / ∂ x^2 = ∂^2 u / ∂ t^2) and the heat equation (c ∂^2 u / ∂

Over which interval is f(x) = x^3 - 12x^2 + 36x + 1 decreasing?

What are the critical value/s for y = x^3 - 3x^2?

Show that the level curves of the cone z = ( x^(2) + y^(2) )^(1/2) and the paraboloid z = x^(2) + y^(2) are circles.

Please see the attached file for the fully formatted problems. Page: - 468 1 and 5 Page 477 and Page 478 1/a,d,c,e,f 2/a,b

(a) Find the solution of the initial-value problem? dy/dx = cos(4x) / 3 − sin(4x), y = 6 when x = 0. (b) (i) Find, in implicit form, the general solution of the differential equation dy/dx = −e^x + e^−x / y(e^x − e^−x + 1)^3 (y > 0). (ii) Find the corresponding explicit form of this g

I have 2 functions I would like to take the total differential of: I= I (R-PI) and C=C(Y-T, R-PI)) Where PI is Pi. If you can walk me through the process, that will help me better understand it and be able to work on other problems

Question Use Runge-Kutta method of order four to approximate the solution to the given initial value problem and compare the results to the actual values. y'=e^(t-y) , 0 <=t <=1 , y(0)=1 with h = 0.5(Interval) Actual solution is y(t)= In((e^t+e-1). For full description of the problem, please see the attached question

I am having problems solving this linear equation. I think it's the sin that is throwing me off. Can you show me how to solve this? dy/dt = 2y + sin 2t

Suppose you wish to model a population with a differential equation of the form dP/dt = f(p), where P(t) is the population at time t. Experiments have been performed on the population that give the following information: ? The population P = 0 remains constant. ? A population close to 0 will decrease. ? A population of P =

See attached file for full problem description. I need following questions to be answered: 1 a,c,d,e,f & 2 (You can Find Problem in the page 451, which is attached).

Question (1) Write the Taylor series with center zero for the function f(x) = In(1 + x^2 ) Question (2) Compute the first-order partial derivatives of f(x, y) = 2x/(x-y) Question (3) Evaluate the double integral (1 to 3)(0 to 1) of (2x-3y)dx dy Question (4) Calculate the divergence and curl of the vector field F(x,

If only 15% of the carbon-14 remains in a fossilized piece of bone, how old is the bone? A(t)= Aoekt I am trying to solve this decay problem the o is a subscript and the k and t are superscripts in the equation. The problem is: if only 15% of the carbon-14 remains in a fossilized piece of bone, how old is the bone? (use 57

Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction of cell walls and is absorbed from foods containing cholesterol: Let C(t) be the amount (in milligrams per deciliter) of cholesterol in the blood of a particular person a

Find the parametric equations that correspond to the given equation: ^ ^ ^ r = t e^(-t) i - 5t^(2) k

Consider the following two collections of data that represent realizations of two random variables X1 and X2: X1: 18.9 21.1 17.8 20.2 16.0 19.0 20.9 19.1 22.5 18.7 15.:3 17.5 22.1 19.8 20.76 X2: 2:3.9 17.8 20.7 20.6 20.0 21.6 25.0 21.9 21.5 20.6 22.0 20.4 2:3.2 21.5 2:3.0 2:3.:3 21.8 2:3.8 26.6 2:3.0 22.0 2:3.8 22.1 (a) Es

1. America creates more garbage than any other nation. According to Denis Hayes, president of Seattle's nonprofit Bullitt Foundations and a founder of Earth Day, "We need to be an Heirloom Society instead of a Throw-Away Society." The EPA estimates that, on average, we each produce 4.4 pounds of garbage daily (Source: Take out

1 Find the particular solution of the following differential equations: A) Given that when t=0, y=3 and dy/dt=0.5 B) Given that when x=0, y=0 and dy/dx=1 2 In a galvanometer the deflection θ satisfies the differential equation: solve the equation for θ given that when t=0, θ=0 and dθ/dt=0 See a

1 Solve the differential equation Given that y=2.5 when x=1 2 Apply the integrating factor method to solve this equation analytically I think the answer should be around 3.4119 See attached file for full problem description.

Use the method of Lagrange multipliers to find the extreme valus of 3x - 4y +12z on the spherical surface with equation x^2+y^2+z^2=1.

1 First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4. 2 Solve the initial value problem dy/dx = y^3 , y(0) = 1 3 Find the center and radius of the circle described in the equation 2x^2+2y^2-6x+2y=3. 4

1. For the problem given below use the convolution theorem to write a formula for the solution of the I.V. problem in terms of f(t) y''-5y'+6y=f(t) y(0) = y'(0)=0 2. Use Laplace Transforms to solve the following equation t^2 y'-2y = 2 (no IC's)

Question (i) Find the vector equation of plane which passes through the points (2,1,1) , (1,-1,-1) and (-1,1,2). Question (2) Obtain the Cartesian equation of a plane passing through three points (3,6,5) , (4,5,2) and (2,3,-1). The question file is attached.