macdude425
Member (again)
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Okay, so I've got this take home test to do by Monday morning. I've got two problems left, and I've hit a brick wall.
Here's what the problems are.
1) Find the first and second derivative, and critical points, of y=(x-1)/(x^2+1)
(Note: the second derivative critical numbers will be discovered using synthetic or long division)
Already got the first derivative on this one, but I keep getting erratic answers on the second one when I try to simplify it.
2) Find the first and second derivatives and critical numbers of y= cos(x) + sin(2x) on [0,2pi]
(hint: to find the critical numbers of the first derivative you will need to use a double angle formula to force a quadratic "type" equation - use the substitution u=sin(x), remember the interval is from [0,2pi] so you might want to consider all the solutions in degrees and then convert to radians)
I already have the first and second derivatives on that second one; -sin(x) + 2cos(2x) and -cos(x) - 4sin(2x) respectively, but I'm not exactly sure WHAT to do from there to get the critical numbers from the first deriv.
Any suggestions?
Thanks.
Here's what the problems are.
1) Find the first and second derivative, and critical points, of y=(x-1)/(x^2+1)
(Note: the second derivative critical numbers will be discovered using synthetic or long division)
Already got the first derivative on this one, but I keep getting erratic answers on the second one when I try to simplify it.
2) Find the first and second derivatives and critical numbers of y= cos(x) + sin(2x) on [0,2pi]
(hint: to find the critical numbers of the first derivative you will need to use a double angle formula to force a quadratic "type" equation - use the substitution u=sin(x), remember the interval is from [0,2pi] so you might want to consider all the solutions in degrees and then convert to radians)
I already have the first and second derivatives on that second one; -sin(x) + 2cos(2x) and -cos(x) - 4sin(2x) respectively, but I'm not exactly sure WHAT to do from there to get the critical numbers from the first deriv.
Any suggestions?
Thanks.