Calculus Answers

what is the centroid of x^2=y, x+y=6, x=0. with solution

Let (u,v)=u^2-v^2,y(u,v)=2uv.

Find the the Jacobian determinant,J(u,v).

Determine which of the following

pairs of functions are independent. Using the Jacobian matrix

a) u= x cos y and v=x sin y;

b)u= x + y and v= y/x+y;

c)u=x-2y and v=x^2 +4y^2-4xy+3x-6y;

d)u= x + 2y and v= x^2-y^2+2xy-x

<e> find the turning points and point of inflection on the curve, y=x⁵-5x⁴+5x³-1

<e> Congratulations! You are hired in a business organization. In this company the market research department that you are the member recommended to manufacture and market a promising new product (x). After extensive surveys, the research department supported the recommendation with the demand function:

Dx = f (p) = 60 – 3 P

Where Dx is quantity demanded at price P during a month. Financial department has brought the cost function and is given by

C(x) = 72 + 6x

Now the team leader of the market research department ordered you to manipulate the following problems.

Express revenue as a function of X

Expresses profit as a function of X

<e> Let f

f be a function such that at each point (x,y)

(x,y) on the graph of f

f, the slope is given by dy

dx

=1

2

x−1

4

y

2

dydx=12x−14y2. The graph of f

f passes through the point (1,−2)

(1,−2) and is concave up on the interval 1<x<1.5

1<x<1.5. Let k

k be the approximation for f(1.3)

f(1.3) found by using the locally linear approximation of f

f at x=1

x=1. Which of the following statements about k

k is true?