anonymous
  • anonymous
Determine if (y=tan x + sec x) has any maximums or minimums for -pi/2 < x < pi/2 and justify your answer.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
jst take dy/dx
anonymous
  • anonymous
y'=sec(x)^2+sin(x), y'=0 when sec(x)^2=-sin(x), solve, profit!
anonymous
  • anonymous
thanks!!

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anonymous
  • anonymous
wait how dou get sin(x)??
anonymous
  • anonymous
Oh, sin(x) was my mistake.
anonymous
  • anonymous
Apparently, I'm still bad at calculus. XP It should be (sin(x))(cos(x)^-2).
anonymous
  • anonymous
i thought derivative of sec x is sec x tan x
anonymous
  • anonymous
yea........
anonymous
  • anonymous
sin(x)/cos(x)^2=tan(x)/cos(x)=tan(x)sec(x)
anonymous
  • anonymous
Same thing. I just didn't remember it, I had to prove it out.
anonymous
  • anonymous
ok so what i do now after i got the derivative ??
anonymous
  • anonymous
sec(x)^2+tan(x)sec(x)=y'=0, tan(x)+1=0, tan(x)=-1, x=arctan(-1)
anonymous
  • anonymous
Woops, my bad. Wait a sec.
anonymous
  • anonymous
(sec(x)+tan(x))=0, tan(x)=-sec(x)
anonymous
  • anonymous
there we go. when do tan(x) and -sec(x) intersect?
anonymous
  • anonymous
wait a minute i need to look at unit circle, i dont have those memorized
anonymous
  • anonymous
sin(x)/cos(x)=-1/cos(x), sin(x)=-1 when is this true?
anonymous
  • anonymous
i think 3pi/4, 7pi/4

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