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Question
Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:
f(x) = x2
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Solution
Given function f(x) = x2
⇒ f'(x) = 2x
For maximum/minimum or critical points,
If f'(x) = 0 then 2x = 0 or x = 0
f'(x) changes sign from negative to positive as it passes through x = 0.
∴ f has local minimum at x = 0.
Local minimum = f(0) = 0
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