Undetermined coefficients

Use the method of undetermined coefficients to solve the attached differential equation (see attachment)

Find a general solution

Find a general solution for the attached

Integration

Decide whether to integrate with respect to "X" and "Y", then find the area of the region. x+y^2=42, x+y=0.

Determining the location of local extremum and the max and min values

The Problem is attached

Finding inflection points and the intervals wher curve is concave up, convave down

Given the function f(x) = x^3 - 6x^2 + 12x Find all inflection points and the intervals where curve is concave up, concave down. Sketch the curve labeling the axes with all extreme points. You may use the second derivative test to determine if a max or min exists at a critical point.

Find the open intervals on which P is increasing or decreasing

problem is attached

Optimization of business and economics

A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to have 1.5 inches, and the margins on the left and right are to be in 1 inch. What should the dimensions of the page be so that the least amount of paper is used?

Critical Points, Max-Min values, inflection points

Given: y = f(x) = 3x4 + 4x3 Find: A. All critical points B. Max - Min Values C. Inflection points D. Where is f(x) concave up E. Where is f(x) concave down F. X and Y intercepts G. Where f(x) is increasing H. Where f(x) is decreasing I. Sketch the curve label

Find the area between the curves

Find the area between the curves y = x2 + x + 1 and y = 2x + 7 From x = -2 to x = 3 Sketch the curve and indicate the interval and the enclosed area

Evaluating Definite Integrals

problem is attached