Find the local minimum value of the function | vedclass

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(A) The given function is $f(x) = 3 + |x|$.Note that the function is not differentiable at $x = 0$,so the second derivative test cannot be applied.We

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$3$

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(A) The given function is $f(x) = 3 + |x|$.Note that the function is not differentiable at $x = 0$,so the second derivative test cannot be applied.We use the first derivative test. The critical point is $x = 0$.For $x For $x > 0$,$f(x) = 3 + x$,so $f'(x) = 1 > 0$.Since the derivative changes sign from negative to positive at $x = 0$,$x = 0$ is a point of local minima.The local minimum value is $f(0) = 3 + |0| = 3$.

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

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