UPSEE 2017 Solved Paper

Given, y=alogex+bx2+x .......(i)
∴

dy

dx

=a×

1

x

+2bx+1 ........(ii)
At the point of maxima,

dy

dx

=0
∴

a

x

+2bx+1=0 .......(iii)
[from Eq. (ii)]
According to question for x=1 and x=2 satisfy Eq (iii)
∴a+2b+1=0 ........(iv)
And

a

2

+4b+1=0 ......(v)
By solving Eqs. (iv) and (v),
a=−

2

3

,b=−

1

6