### Problems I Can't Fix in the Lecture Hall

Yesterday one of my students from the Calculus Circus came by my office hours. We were working on a problem of finding the critical points of

And then in an attempt to solve it, he tried the usual incorrect strategy selected by students who can't do algebra.

3

I stopped him before he factored out the

He said, "I don't know."

I explained that "I don't know" is usually unsuccessful in algebra and pointed out that this is a quadratic equation there are only two ways he should consider solving a quadratic equation: factoring or the quadratic formula.

He's probably going to go back to doing things the wrong way. But this is the type of misconception that I can't fix in a lecture hall.

*f*(*x*) =*x*^{3}+ 3*x*^{2}- 45*x*+ 10. He correctly found the derivative,*f*'(*x*) = 3*x*^{2}+ 6*x*- 45. At my direction, he set it equal to zero: 3*x*^{2}+ 6*x*- 45 = 0.And then in an attempt to solve it, he tried the usual incorrect strategy selected by students who can't do algebra.

3

*x*^{2}+ 6*x*= 45I stopped him before he factored out the

*x*and asked, "What technique are you using to solve this equation?"He said, "I don't know."

I explained that "I don't know" is usually unsuccessful in algebra and pointed out that this is a quadratic equation there are only two ways he should consider solving a quadratic equation: factoring or the quadratic formula.

He's probably going to go back to doing things the wrong way. But this is the type of misconception that I can't fix in a lecture hall.