QJEEM21Ma11ed: JEE Main 2021 Mathematics - Class 12 JEEM21Ma11ed Solution: Let a function g : [ 0, 4 ] → R be defined as g ( x ) = { max 0 …

Question

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Let a function g : [ 0, 4 ]

\to

R be defined as

g (x) = {\begin{matrix} max_{0 \leq t \leq x} {t^{3} - 6 t^{2} + 9 t - 3), & 0 \leq x \leq 3 \\ 4 - x, & 3 < x \leq 4 \end{matrix}

, then the number of points in the interval (0, 4) where g(x) is NOT differentiable, is ____________.

Accepted Answer

f (x) = x^{3} - 6 x^{2} + 9 x - 3

f (x) = 3 x^{2} - 12 x + 9 = 3 (x - 1) (x - 3)

f (1) = 1

,

f (3) = 3

g (x) = [\begin{matrix} f (9 x) & 0 \leq x \leq 1 \\ 0 & 1 \leq x \leq 3 \\ - 1 & 3 < x \leq 4 \end{matrix}

g(x) is continuous

g^{'} (x) = [\begin{matrix} 3 (x - 1) (x - 3) & 0 \leq x \leq 1 \\ 0 & 1 \leq x \leq 3 \\ - 1 & 3 < x \leq 4 \end{matrix}

g(x) is non-differentiable at x = 3

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