Question

Hello OpenStudy Friends!
WITHOUT using a calculator, find one critical value for the function y = tan(x)

Answer 1

I know I have to find the first derivative, which is y' = 1 + sec^2(x).

Answer 2

I then try setting it to zero and move the 1 over making it negative.

Answer 3

from there I'm lost...

Answer 4

y' of tan(x) is (sec^2(x)) not (1+ sec^2(x))

Answer 5

oh sorry, it's y = x + tan(x)

Answer 6

sec^2(x) = -1

sec(x) = sqrt(-1)

so this implies that there are no real numbers x that make sec^2(x) + 1 = 0 true

Answer 7

looks good to me.

Answer 8

would finding the inverse value help anything? what does that do anyway?

Answer 9

well the inverse secant of sqrt(-1) isn't defined (I don't think anyways)

it could be defined in some strange way, but idk

Answer 10

if you're only considering real numbers for x, then there are no solutions to sec^2(x) + 1 = 0

so there are no critical numbers

Answer 11

awesome thnx

Answer 12

np