Hello Everyone, In class, I am given to show that maximizing over x1 first and then maximizing over x2 for f(x1,x2) is the same as maximizing x2 first and then maximizing over x1 for f(x1,x2), assuming f(x1,x2) is always continuous. Graphically, this statement is apparent to me, because maximizing over x1 first for f(x1,x2) means to find a… Show more

The definition of a critical point is where both the partial derivatives (wrt x and wrt y) equal 0. You cannot take the derivatives separately. If you have a radially symmetric surface, you will luck out and be ok, but for something lacking that symmetry, you most likely not find any maximum, let alone a global max. For instance, plot up f(x,y)…

To whom it may concern; I am a first-semester community college student. Due to a low score, I am in Basic Math. The reason for this is that I am 46 years old, and have forgotten some of the concepts due to lack of use. I was checking out the Math Community but found that the Math files were Linear Algebra and above. Do you have anything for a… Show more

Hi Sean, Thank you for your note. Unfortunately, we do not have resources that is specific to your inquiry. The closest we may have is our Reconceptualizing Mathematics by Sowder, Sowder, and Nickerson. It is written for future elementary school teachers, and as such discusses the concepts of mathematics. The LaunchPad (online homework platform)…

Has anyone done a pacing guide for Statistics and Probability with applications 3e? We are a trimester school, students will take on-level stats two of three trimesters. Each trimester is about 56-58 teaching days.