The other day I had a fairly popular post talking about how mathematicians easily and often admit that they don't know things or don't understand things. Today at work a real-life example came up!

Original post linked to in the next toot since apparently I can't post a link and have an image at the same time ... wtf?!

I was helping a student with Calc I in my office. The question gave a function and asked for values of x where the tangent line was horizontal. The function is the first in the image.

This requires taking the derivative with the product rule. The result of this is the second in the image. Since the second term has a denominator (other than 1 of course) we need to combine the two terms so we can set the numerator to 0 and solve.

The result of this operation is the third in the image. Fractions are 0 when their numerators are 0, so the fourth line shows the equation to be solved.

The student got this far without any help but was unable to solve the equation. This is commonplace. After all, the hardest part of calculus is algebra. But I couldn't see how to solve it either, so I told the student this.

At this moment two of my colleagues were talking in the hall outside my office so I told the student I'd ask them about it. Neither knew how to solve it and told me as much. So I told the student, who was actually thrilled that none of us could solve it either.

So I asked Wolfram Alpha, which gave a solution using the Lambert W, aka the productlog function. I'm a combinatorial topologist -- I do graph theory of various kinds. I've heard of this function but otherwise know nothing at all about it. And I'm happy to admit it! Anyway, that's how mathematicians roll.

ETA: Of course this problem shouldn't have appeared in an introductory calculus text since no undergraduate at that level would be able to solve it, so its inclusion was a mistake of the author or the editor.

#Calculus #LambertW #HorizontalTangent #DifferentialCalculus #Math #Mathematics #Mathematicians