AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper

v=4x2+2x−8
differentiate w.r.t. x′ on both sides,
‌

dy

dx

=4(2x)+2(1)
‌

dy

dx

=8x+2 ...(i)
y=x3−x+13
differentiate w.r.t. ' x′ on both sides,
‌

dy

dx

=3x2−1...(ii)
Since, curves are touch each other
⇒‌‌8x+2=3x2−1
⇒‌‌3x2−8x−3=0
⇒‌‌(x−3)(3x+1)=0
⇒‌‌x=3 (or) ‌

−1

3

Put, x=3 in y=x3−x+13
y=33−3+13
y=37
∴ Point of contact P=(3,37)