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Q.
Total number of points of non differentiability of $f(x) = $ min.$\{1, 1 + x^3, x^2- 3x + 3\}$ is ______.
Continuity and Differentiability
Solution:
$y = x^2 - 3 x + 3$ and $y = 1$,
when $x^2 -3 x + 3 = 1$
or $x^2-3 x + 2 = 0$
or $x = 1,2.$
$y = x^3+ 1$ touches
$y = 1$ at $x = 0$.
Further $= x^3 + 1$ and $y -x^2- 3x + 3$
intersect at only one point.
From the graph $f(x) =$ min.$\{1, 1 + x^3, x^2- 3x + 3\}$
is non-differentiable at $x = 1$ and $x = 2$.
