KEAM 2013 Math Paper

Given curve is
y=3x2+ax3
On differentiating w.r.t. x, we get
‌

dy

dx

=6x+3ax2=m( say ) ....(i)
Now, differentiating Eq. (i) w.r.t. x, we get
‌

dm

dx

=6+6ax
and ‌

d2m

dx2

=6a
For maximum or minimum of m,
put ‌‌‌

dm

dx

=0⇒6+6ax=0
⇒‌‌x=−‌

1

a

<0 0 (max)
But given m is maximum at x=‌

1

2

.
∴‌‌−‌

1

a

=‌

1

2

⇒a=−2