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Question Number 13955 by ajfour last updated on 25/May/17
$y(x)= { ((4+6x−3x^2 ; x < 2)),((2x^2 −14x+20 ; x ≥ 2)) :} Is the function y(x) differentiable with respect to x at x=2 ?$
$y (x) = {\begin{cases} 4 + 6 x - 3 x^{2}; x < 2 \\ 2 x^{2} - 14 x + 20; x ⩾ 2 \end{cases}$ $I s t h e f u n c t i o n y (x)$ $d i f f e r e n t i a b l e w i t h r e s p e c t t o x$ $a t x = 2 ?$
Commented byprakash jain last updated on 25/May/17

$\lim_{x \to 2^{-}} y (x) = 4 + 12 - 12 = 4$ $\lim_{x \to 2^{+}} y (x) = 8 - 28 + 20 = 0$ $y (x) is not continous at x = 2 .$ $Hence not differentiable .$
Commented byajfour last updated on 25/May/17

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