Application Of Derivatives Ques 74
74. If $f(x)=\begin{aligned} & |x| \text {, for } 0<|x| \leq 2 \\ & 1\end{aligned}$, for $\quad x=0$. Then, at $x=0, f$ has
(a) a local maximum
(b) no local maximum
(c) a local minimum
(d) no extremum
$(2000,1 \mathrm{M})$
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Answer:
Correct Answer: 74.(a)
Solution:
Formula:
Maxima and Minima of functions of one variable :
It is clear from the figure that at $x=0, f(x)$ is not continuous.
Here, $f(0)>\text{RHL at }x=0$ and $f(0)>\text{LHL at }x=0$
So, local maximum at $x=0$.
BETA
