Find all values of x on the interval 0

Question

Find all values of x on the interval 0<=x<=2Pi for which the graph of y=cos(x^2-1) has a horizontal tangent. Find all values of x on the interval 0<=x<=2Pi for which the graph of y=cos(x^2-1) has a horizontal tangent. @Mathematics

anonymous · Answer

i got this far y'=-2Xsin(x^2-1)

amistre64 · Answer

good, and when does that equal zero?  which is the slope of a horizontal line

amistre64 · Answer

-2x = 0

sin(x^2-1) = 0

both are valid for solving

anonymous · Answer

i didnt know i can separate -2x from sin =) so is the answer just x=0,x=1,x=-1?

amistre64 · Answer

:)  its not so much as separating as seeing that if either of those goes to zero, the value of the whole goes to zero.

-2x(0) = 0

0 sin(x^2-1) = 0

but yeah, 0 and -1 and 1 all look good

amistre64 · Answer

we got a zero for sin(pi) as well

amistre64 · Answer

-1 doesnt count since its not between 0 and 2pi

anonymous · Answer

i can really tell interval 0<=x<=2Pi

anonymous · Answer

can't

amistre64 · Answer

|dw:1321049566307:dw|

amistre64 · Answer

since x=-1 is not in that interval, we scrap it

amistre64 · Answer

x^2 - 1 = pi  is an option

anonymous · Answer

how do you know thats an option?

amistre64 · Answer

becasue sin(pi) = 0

anonymous · Answer

thanks a lot