Question

Calculus:
Find the critical numbers for f(x) = 2sec(x)+tan(x) on the interval 0<=x<2pi (0<=360)

I'm stuck x.x

Answer 1

how far have you gotten so far?

Answer 2

All I really did was rewrite the equation as
f(x)= 2/cosx + sinx/cosx

What should I do next? sec having critical numbers at multiples of pi/2, tan also??

Answer 3

what do you get for f'(x)? how to get critical points from that f'(x) show your work, please

Answer 4

actually.. using the original form was easier,
f'(x) = 2secxtanx+secx^2

but then how would I get the critical numbers? I

Answer 5

factor sec out,

Answer 6

you get sec (2tanx +sec) =0 so, sec =0 or 2tan +sec =0
however, sec =1/cos therefore, it never be 0, so you just have 2tan +sec =0. it is
\[2\frac{sin}{cos}+\frac {1}{cos}=\frac {2sin+1}{cos}\]it is =0 iff 2sinx +1 =0 ,
sinx = -1/2
x = ??? that is your critical points. plug them ( if there are more than 1 solution) into original function to get value of critical points. that's all you need

Answer 7

tag other if you have more question, please. Sorry for that. I want to eat something. hehe

Answer 8

Ah, thanks! I got 3/sqrt(3) and -3/sqrt(3) as my final answer. is it correct?