Using Lagrange multipliers to find extrema of (f) subject to the 2 constraints.

Minimize f(x,y,z)=x^2+y^2+z^2 with constraints x+2z=6 and x+y=12. Assume x,y,z are nonnegative.

Find critical points and test for relative extrema.

List the critical points for which the second partials test fails. f(x,y)=x^3+y^3-6x^2+9y^2+12x+27y+19

Vector Calculus

f(x,y) = x^3 + y - xy + 1 a) Are there points on the curve y = (x - 1)^2 where Gradient f is perpendicular to the curve? b) Find the absolute maximum and minimum of the function in the region 1 >= x >= 0 and y >= 0.

Extreme Values, Differentials and Maximizing Areas

1) Find the absolute extreme values of the function f(x,y) = x^2 + xy - x - 2y + 4 on the region D enclosed by y= -x, x=3, y=0 2) Given a circle of radius R. Of all the rectangulars inscribed in the circle, find the rectangular with the largest area. 3) a) Find the differential df of f(x,y)= x(e^y) b) use the differenti ...continues

Polynomials that satisfy a formula.

Consider the formula (f X g)'(x) = f'(x)g'(x). When do polynomials f and g satisfy the formula?

projectile motion

With this problem im seeking a detailed explanation. I already have some of the answers however i dont see how they were obtained. Can you please solve this and show me how each answer was obtained. My numbers are way off from what they should be. Thanks The quarterback of a football team releases a pass at a heigh ...continues

calc. III vectors

Find the vectors T, N, and B at the given point. r(t)= , (1,0,1) I'm having problems with this one because it requires lots of calc. I and II and i just can't remember how to do some of this. I can take the first derivative and the second but doing the cross product is giving me trouble.

Derivatives and Differentiation of Functions: Rate Change in Radius of a Sphere

A spherical baloon is being inflated at a rate of 400 cubic cm/min. At what rate is the radius changing when the radius is 25 cm. GIVEN (V=4/3*pi*r^3)

Derivatives and differentiation: Rate of Change - Surface Area of a Cube

At what rate is the surface area of a cube changing the edge measures 5 inches and is changing at a rate of 2 in/min. GIVEN (A=6*s^2)

Function : Horizontal Tangent Line

Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5