Thread: Optimazation Problems

This one is killing me:

Find the point on the line y = 4x + 7 that is closest to the origin.

I keep trying the distance formula and I end up with:
d = [ 17x^2 + 56x + 49]^1/2
because I substituted for y, getting it down to two variables like my teacher said. The solutions manual keeps saying I'm wrong because after I differentiate that I get a different answer. They do something weird where they square it and then differentiate to make it easier to work with. I get an ugly looking fraction when I differentiate my findings.

Set D' to 0.







Are you getting this?