y-x-4-6x-3x-2-x-lt-2-2x-2-14x-20-x-2-Is-the-function-y-x-differentiable-with-respect-to-x-at-x-2-

Question Number 13955 by ajfour last updated on 25/May/17

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 by prakash 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 by ajfour last updated on 25/May/17

v e r y t r u e, t h a n k s S i r .

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