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ID:
Class: 12
Subject: Math
Topic: Application of Derivative
Type: Short
Question:
Find the local maxima and local minima, if any, of the function \( f(x) = x^2 \). Find also the local maximum and the local minimum values.
Official Solution
Explanation:
We have:
\[
f(x) = x^2 \Rightarrow f'(x) = 2x
\]
Setting \( f'(x) = 0 \Rightarrow x = 0 \)
Also,
\[
f''(x) = 2 > 0
\]
So, \( x = 0 \) is a point of local minima.
Local minimum value is:
\[
f(0) = 0
\]
There is no local maximum.
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