Calculus Answers

The combined dimensions of a passenger's carry on bag may not exceed 45 inches. That is the length, width and height of the suitcase can add up to at most 45 inches. Find the maximum volume of a rectangular suitcase that meets these requirements.

Find the extreme values of the function f(x,y) = 2x^2 + 3y^2 - 4x - 5

on the set D = {(x,y) : x^2 + y^2 < or = 16 }

Use Lagrange multipliers to find the maximum and minimum values of the function ( if they exist) subject to the specified constraint.

f(x,y) = 4x^2 + 9y^2 on the hyperbola xy = 6

1. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change of the area when the radius is 3 cm long

Calculate the mean value of f(x)=3x²+4x+1 between x = −1 and x = 2 

Find the inverse of the given function.

h(x)=sin^-1 sqrt x

Identify a mathematician that contributed to the development of theory of functions in Mathematics. State the contribution made and why was it so important to the field of Mathematics. 

Can a quadratic function have a range of (- ∞, ∞)? Justify your answer.

b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect?

 c. Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are not included.

If a third degree polynomial has a lone x-intercept at x = a, discuss what this implies about the linear and quadratic factors of that polynomial.