If y=a x+b x^2+x has its extreme value at x=-1 and x=2 , then the value of a + b is

Step-by-step solution

aligned & y=a x+b x^2+x & d y d x = a x +2 b x+1 & ( d y d x )_ x=-1 =-a-2 b+1=0 & a+2 b=1...(i) aligned and ( d y d x )_ x=2 = a 2 +4 b+1=0 aligned & a+8 b+2=0 & a+8 b=-2...(ii) aligned Solving (i), (ii) we get array cc & b= -1 2 and a=2 & a+b=2+ ( -1 2 )= 3 2 array