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The function y=(ax+b)/(x-1)(x-4) has tur...

The function y=`(ax+b)/(x-1)(x-4)` has turning point at P(2,-1) Then find the values of a and b.

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`y=(ax+b)/(x-1)(x-4)=(ax+b)/(x^(2)-5x+4)` has turning point at p(2,-1)
Thus , P(2,-1) lies on the curve .Therefore , 2a + b =2
Also , `(dy)/(dx)`=0P(2,-1)
Now `(dy)/(dx)=a(x^(2))-(5x+4)-(2x-5)(ax+b)/(x^(2))-(5x+4^(2))`
At P(2,-1),`(dy)/(dx)=(-21+2a+b)/(4)=0`
or b=0 or a=1
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