Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 7y cos(x),    0 ≤ x ≤ 2π

Given the differential equation y’’ +5y’+6y=te^t with start value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of y(t).

a) Find an expression for Y(s)

b) Find the solution to the equation by using inverse Laplace transform.

1)Select all that applies to the Fourth-order Runge-Kutta (RK4) method K subscript

1 equals f left parenthesis t subscript k comma y subscript k right parenthesis K subscript

2 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 1 right parenthesis K subscript

3 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 2 right parenthesis K subscript

4 equals f left parenthesis t subscript k plus h comma space y subscript k plus h space K subscript 3 right parenthesis

2) y subscript k plus 1 end subscript equals ? Select one or more:

A. - It has four function evaluations - and y subscript k plus 1 end subscript equals y subscript k plus space left parenthesis 1 third space K subscript 1 plus 2 over 3 space K subscript 2 plus 2 over 3 space K subscript 3 plus 1 third space K subscript 4 right parenthesis space h over 2

B. - It is a fourth-order accurate method - and it has seven function evaluations

C. All of the above.

D. K subscript 1 comma space K subscript 2 comma space K subscript 3 space a n d space K subscript 4 are also called slopes of the solution curve or integral curve.

E. The method is named after two German Mathematicians Runge and Kutta.

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(6​,-13​), endpoint ​(14​,-10​)

Given the function u(p,q,r)=((p-q)/(q-r)), with p=x+y+z,q=x-y+z, and r=x+y-z, find the partial derivatives au/ax=, au/ay=, au/az=

I need to know the inflection and to be able to explain how I got the answer please

How are the column space and the row space of a matrix A related
to the column space and row space of its reduced row echelon form?
How does this prove the column rank of A equals the row rank?

A fisherman can row upstream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip too 6 hours?

The distance the fisherman rowed in ----- miles
     (Type an integer or a decimal)

Let f(x) be differentiable on the interval [a,b]. Select all of the following statements which must be true.

1. f(x) must attain its maximum value on the interval [a,b]

2. There is some number c in the interval (a,b) such that f′(c)= (f(b)−f(a))/ (b−a)

3. f(x) is integrable on [a,b].

4. f(x) is continuous on (a,b).

5. f(x) is a polynomial.

6. f(x) is an increasing function.

If the instantaneous value of a voltage in an AC circuit of the communication system (at any time t seconds) is given by V= 142sin(8πt-0.125π) volts, determine:

1). Given that the voltage waveform can also be represented as V=Rsin(ωt+θ), use compound angle identities to resolve the resultant voltage waveform into its two component waveforms: asinωt and bcosωt.

2). In another circuit the voltage, V is made up of two components v1 = (A/3)Sin(t) and v2 = (A/2)Cos(t). Sketch the two component waveforms and the resulting waveform V= (A/3)Sin(t) + (A/2)Cos(t) on the same axes and estimate from your graph the equation of the combined waveform. Also analytically calculate, showing all your working, the parameters (R&θ) of the equation of the combined waveform if represented as V=Rsin(Ѡt+θ), giving θ in radians.

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is perpendicular to u. Then find a vector w which is perpendicular to both u and v. Explain the reason for your selection clearly.

2. Find the slope of the tangent line to the parametric curve x = 5 + sin(3θ) and y = −3 + 2tanθ at θ = π.

1.Determine the linearization of

f(x)= −2.0 x^2.0−4.0 x - 4

at x=2.

2.Determine the linearization of f(x)= (−x^2)−4/x^3 at x=−1.