The function `f(x)` is defined by `f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x<2 ,\ \ \ \ \3x+2\ \ \ ,\ \ \ 2lt=xlt=4 ,\ \ \2a x+5b\ \ \ ,\ \ \ x>4` f is continuous them determine the value of a and b

Explanation

Thie function is continuous at `x=2`



`lim _{x -> 2} f(x)=lim _{x -> 2^{+}} f(x)=f(2)`


`lim _{x -> 2} x^{2}+a x+b=lim _{x -> 2} 3 x+2 `


`4+2 a+b=6+2 `


`2 a+b=4 ldots ldots(1)`



Given function is also continuous at `x=4`.


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