(C) To find the local maxima and local minima,we analyze the function $f(x)$ in its given intervals:$1$. For $-3 < x \leq -1$,$f(x) = (2+x)^3$. The de

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(C) To find the local maxima and local minima,we analyze the function $f(x)$ in its given intervals:$1$. For $-3 $2$. For $-1 $3$. At $x = 0$,$f'(x)$ is undefined. For $x 0$,$f'(x) > 0$ (increasing). Thus,$x = 0$ is a local minimum with $f(0) = 0$.$4$. Comparing the values,we have a local maximum at $x = -1$ and a local minimum at $x = 0$.Therefore,the total number of local maxima and local minima is $2$.

Class 12 Mathematics Applications of Derivatives Maxima and Minima

Find the total number of local maxima and local minima of the function $f(x) = \begin{cases} (2+x)^3, & -3 < x \leq -1 \\ x^{2/3}, & -1 < x < 2 \end{cases}$

IIT 2008 All IIT

A
$0$
B
$1$
C
$2$
D
$3$

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Find the total number of local maxima and local minima of the function $f(x) = \begin{cases} (2+x)^3, & -3 < x \leq -1 \\ x^{2/3}, & -1 < x < 2 \end{cases}$

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