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jesuslovesu
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Homework Statement
Use the Taylor series about x = a to verify the second derivative test for a max or min. Show if f'(a) = 0 then f''(a) > 0 implies a min point at x = a ... Hint for a min point you must show that f(x) > f(a) for all x near enough to a.
Homework Equations
The Attempt at a Solution
f(x) = a0 + a1(x-a) + a2(x-a)^2 + ...
f'(x) = a1 + 2a2(x-a) + ...
f''(x) = 2a2
f'(a) = a1
if a1 = 0 then it's either a max or min
but I don't quite know what I should do to show that if f''(a) > 0 or < 0 that the point will be a max or min.
Should I do a limit?
[tex]\lim_{x \to a} a\right0 + a\right1 (x-a) + a\right2(x-a)^2 ... > a\right0 [/tex] ?
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