Question

The local minimum value of the function $f$ given by $f(x)=3+|x|,x\in R$ is

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

Answer: (C)

Note that the given function is not differentiable at $x=0$. So, second derivative test fails. Let us try first derivative test.
Note that 0 is a critical point of $f$. Now to the left of 0 , $f(x)=3-x$ and so $f^{\prime }(x)=-1<0$. Also to the right of $0_{1}f(x)=3+x$ and so, $f^{\prime }(x)=1>0$. Therefore, by first derivative test, $x=0$ is a point of local minima of $f$ and local minimum value of $f$ is $f(0)=3$