1.

If the function f(x)={{:(ax+b, -ooltxle2),(x^(2)-5x+6,2ltxlt3),(px^(2)+qx+1,3lexleoo):} is differentiable in (-oo,oo), then :

Answer»

`a=-1,p=-(4)/(9)`
`b=2,Q=(5)/(3)`
a=1, b=2
`a=-1, q=-(5)/(3)`

SOLUTION :Differentiable `implies` continuous
Continuouns at `x=2implies2a+b=0`
Continuous at x=3
`0=9p+3q+1`
Differntiable at x=2
`a=2xx2-5impliesa=-1`
Differentiable at x=3
`2xx3-5=2pxx3+qimplies6p+q=1`
`a=-1,b=2,p=(4)/(9),q=-(5)/(3)`


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