- #1
Qube
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Homework Statement
http://i.minus.com/jZdpOtdOiChOn.jpg
Homework Equations
Local extrema can be determined using the first derivative test.
The Attempt at a Solution
I ran the first derivative test to find the critical points, which were 0 and plus/minus 0.5. I plugged in the values into the original equation. x = 0 makes the function go to infinity, so x = 0 can be ruled out as any sort of local extrema. x = 0.5 makes the function = 2sqrt(e), while x = -0.5 makes the function = -2sqrt(e). Naively, I chose D, which pegs x = 0.5 as the local maximum, which makes sense, doesn't it?
Unfortunately the formal definition of a local maxima is that the sign of the first derivative changes from positive to negative, and in the case of x = 0.5, the opposite happens; the sign actually flips from negative to positive around it, making it a local minima.
I'm assuming this is the correct explanation.
Who else would have fallen for this? Let's be honest :P.
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