Calculus Answers

The temperature in space given by T(x, y, z)= 200xyz? Find the hottest temperature on a unit sphere centered at the origin. (DO NOT USE LAGRANGE MULTIPLIERS)

Find the extreme values of z on the surface 2x^2 + 3y^2 + z^2 – 12xy + 4xz = 35.(DO NOT USE LAGRANGE MULTIPLIERS)

2. a) Find the derivatives of the following functions with respect to x.

X^3+Y^3=3

Y= (sin x) ^tan x

The drawing below shows a square with side a. A straight line intersects the square and encloses

an area A. The heights x and y on the left and right side (in a distance d from the square) of

the intersecting line can be varied. Assuming that x  y and x; y  a, nd an expression for

the enclosed area A(x; y) with respect to x and y.

Give an example of a function of two variables such that f(0,0) = 0 but f is NOT continuous at (0,0). Explain why the function f is NOT continuous at (0,0).

It's time to tidy up your work desk. you are given 27cm^2 of cardboard to build a rectangular box without a lid to store small electronic components. By using the knowledge of partial derivative, determine the maximum volume of this box

The derivative of a differentiable function ff(xx) is given as

ff′

(xx) = xx + 3

(xx − 2)2 .

a. Find intervals of increase and decrease for ff(xx).

b. Determine values of xx for which relative maxima and minima occurs on the graph of

ff(xx).

c. Find ff′′(xx) and determine intervals of concavity for the graph of ff(xx).

d. For what values of xx do inflection points occur on the graph of ff(xx).

The drawing below shows a square with side a. A straight line intersects the square and encloses

an area A. The heights x and y on the left and right side (in a distance d from the square) of

the intersecting line can be varied. Assuming that x  y and x; y  a, nd an expression for

the enclosed area A(x; y) with respect to x and y.

n the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the

angle α = angle BAD which minimizes the distance L, where L = AD + ED

c) Describe geometrical meaning of definite integral with figure.