If $f (x) = \{\begin{array}{cll} Min \{2 - x^{2}, - x^{3}\} & : - 2 \leq x < 0 \\ x | x | & : 0 \leq x < 1 \\ 3 - x & : 1 \leq x \leq 2 \end{array}$ now match the following
Column I Column II
A. The number of critical points of f(x) in [-2, 2] is P. 1
B. The length of the longest interval in which f(x) satisfies Rolle's theorem is Q. 2
C.The number of values of ‘c’ of Rolle's Mean value theorem R. 3
D. The maximum value of f(x) in [-2, 2] is S. 0

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Solution

$\begin{array}{l} f (x) = \{\begin{cases} 2 - x^{2}, - 2 \leq x < - 1 \\ \begin{matrix} - x^{3}, - 1 \leq x < 0 \\ x^{2}, 0 \leq x < 1 \\ 3 - x, 1 \leq x \leq 2 \end{matrix} \end{cases} \end{array}$

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Column I	Column II
A. The number of critical points of f(x) in [-2, 2] is	P. 1
B. The length of the longest interval in which f(x) satisfies Rolle's theorem is	Q. 2
C.The number of values of ‘c’ of Rolle's Mean value theorem	R. 3
D. The maximum value of f(x) in [-2, 2] is	S. 0