This morning I was trying to come up with some good problems for students to use to find local maxima and minima. It's an awesome feeling to be able to combine everything I know about graphs and polynomials and end behavior to create polynomials within the window that I want that do what I want. It's cool to think that I don't have to just guess random things. So the graph is too long and skinny? I can do a vertical compression or a horizontal stretch. I want two local maxes and one local minimum, so I know I need to give it a negative leading coefficient and an even degree. It might be neat to come up with some sort of guidelines and have the students come up with their own polynomials. I wouldn't want them to just guess and check though. I might have them write something that says what they would have to do to a graph to get the desired results. It really forces you to use everything you know about polynomials and graph behavior and actually apply it.
God Loves Math: In which I select a random Bible verse from a random Bible verse generator ( this one ) and ask God to show me a new way of understanding Him, honoring Him, and loving Him while using a mathematical mindset to approach the section of scripture. Today's Random Bible Verse Hebrews 3:4 "For every house is built by someone, but God is the builder of everything." Oh, this verse is full of meaning when considered mathematically! (Although we see it much more when we look at it in its context.) Hebrews 3:1 tells us to fix our thoughts on Jesus, "whom we acknowledge as our apostle and high priest." Why should we do that? "Let's prove Jesus deserves it," is essentially the approach taken by the author. I can appreciate a good proof. 1) If someone is faithful, then they deserve honor. We know this is true because the Bible talks about Moses being found worthy of honor because he was faithful "in all God's house." 2) If Jesus...
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