3. Find the local maxima and local minima, if any, of the following functions. Find
also the local maximum and the local minimum values, as the case may be:
i) f ( x) = x^2

Answers (1)

Given function is
f ( x) = x^2\\ f^{'}(x) = 2x\\ f^{'}(x) = 0 \Rightarrow 2x = 0 \Rightarrow x = 0
So, x = 0 is the only critical point of the given function
f^{'}(0) = 0\\  So we find it through the 2nd derivative test
f^{''}(x) = 2\\ f^{''}(0) = 2\\ f^{''}(0)> 0
Hence, by this, we can say that 0 is a point of minima
and the minimum value is
f(0) = (0)^2 = 0
 

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