Find all zeros of the polynomial function. Use the Rational Zero​ Theorem, Descartes's Rule of​ Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root.

f(x)=2x⁴-17x³+13x²+53x+21

The zeros of the function are?

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $6/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?

Solve the following IVP specifically using the Laplace transform method

(d^3)x/d(t^3)+x=e^(-t)u(t)    f(0)=0 f'(0)=0    f''(0)=0

where u(t) is the Heaviside step function

I am stuck on these:

Find or Calculate the derivative of the function.

y = (x^0.3 − 3x − 6)(x⁻¹ + x⁻²)

f(x) = (6.4x − 6)⁻² + (4.3x − 1)⁻²

f(x) =

h(x) = 4^{x2 − x}

r(x) = ln(x + 1) + 3x⁹e^x

Describe the level surfaces of G(x,y, z) = 1 – y^2 – z. Make sure to provide all the following: their equations, types, plots, and a short word description of their geometric shapes.

Find the constants a, b, c, d, e, r0, r1 for the ellipse r =15/(3−2cosθ) and sketch the graph.

1.38.5. One diagonal of a quadrilateral bisects the other if and only if the diagonal also bisects the quadrilateral.

Last year, 292 million music CDs were purchased by 112 million households in the United states.On the average, how many CDs were purchased in each household

Let F(x, y, z)  =  (6x⁵ ln(5y² + 3) + 10z⁴) i  +  ((( 10yx⁶)/(5y² + 3))+ 8z) j  +  (40xz³ + 8y − 6π sin πz) k
and let  r(t)  =  (t³ + 1) i  +  (t² + 2) j  +  t³ k ,  0  ≤  t  ≤  1. Evaluate  

F · dr (please explain steps, thank you :)

PopSolution Inc is a small IT Solution company based in Central Jakarta, Indonesia. They have just finished their sales pitch meeting with their latest potential client, an automobile sales company based in South Jakarta. The company was very satisfied with their portofolios, and asked them to provide a final quotation on the price that will be agreed upon. As for the project detail, the client asked for a simple web application with 3 main functions: (1) a homepage showing the company’s credibility and location, (2) a page to list all cars the company is selling, and (3) a Contact Us page where future customers can fill their data to further be contacted by the company’s representatives. Since the transaction is too substantial to be handled in the application, all purchase will be done outside of the web application. Every month, PopSolution spends 30.000.000 IDR for the overhead cost of all its employees. The organizational average productivity for the system of similar type is 25 FP/person-month. This means that with one person doing the job of 50 Function Point, it will take one month, with 2 persons doing the job, it will take half a month to finish. As the new member of the development team, you are asked to prove your expertise on software estimation by providing the team with Function Point Analysis (FPA) on your next internal meeting. Your tasks are:

Calculate the Unadjusted Function Point, Value Adjustment Factors, and the Function Point.

9) Suppose that t years from now, one investment will be generating profit at the rate of P 1 ′ = 40 + t 2 hundred dollars per year, while a second investment will be generating profit at the rate of P 2 ′ ( t ) = 100 + 4 t hundred dollars per year. For how many years does the rate of profitability of the second investment exceed that of the first? Compute the total net excess profit for the time period.

Suppose that ac + bd = 0. Show that vectors [a, b] and [c, d] are perpendicular. The number ac + bd is called the dot product of the vectors [a, b] and [c, d].

Show all your work. Let f(x) = x 5 e x 3 (i) Use the Taylor series for e x around 0 to find the Taylor series for f(x) (ii) Use (i) to find f (20)(0), f (21)(0), f (22)(0), f (23)(0)