Question

12. What value of c make the function f(x) = (x2 – 3x when x > 2 continuous when x = 2? 14x + 2c when x < 2 a)-5 b)-3 c) 0 d) 1

Answer 1

f(x) \x2 – 3x when x > 2 14x + 2c when x < 2

Function is continuous at $x=1$

lim f (x) = lim f (x) +2+ +2

$\lim_{x\rightarrow 2^{-}}f\left ( x \right )=\lim_{x\rightarrow 2^{-}}\left ( x^{2}-3x \right )$

$= 2^{2}-3\times 2$

$\lim_{x\rightarrow 2^{+}}f\left ( x \right )=\lim_{x\rightarrow 2^{+}}\left ( 4x+2c \right )$

$=4\times 2+2c$

$=8+2c$

$\lim_{x\rightarrow 2^{-}}f\left ( x \right )=\lim_{x\rightarrow 2^{+}}f\left ( x \right )$

$\Rightarrow -2=8+2c$

$2c=-2-8=-10$

$c=\frac{-10}{2}=-5$

Correct option is

$\boldsymbol{a)-5}$

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