Finding Where the slope is Undefined
So I was helping a student with a problem today. The answer we tried to submit was wrong and I'm not sure I understand why.
The question was:
Find where the slope is undefined for x = 4sec(y)
At first I thought this was fairly straightforward:
We implicitly differentiated, getting:
1 = 4y'sec(y)tan(y)
Then solved for y':
y' = 1/(4y'sec(y)tan(y))
Now I assumed that the slope should be undefined wherever the denominator was zero:
4sec(y)tan(y) = 0
sec(y)tan(y) = 0
Both sec(y) and tan(y) should be zero for the same values of y, namely:
y = pi/2 + k*pi
But this was the wrong answer! I'm worried it might have something to do with the fact that we're dealing with y instead of x, but I was stumped as to how to proceed.