APPLICATIONS OF DIFFERENTIATION
----------------------------------------------------- Tangent & Normal ------------------------------------------------1. (78/14 O) Find the equation of tangent to the curve y   x  1 at the point (3,4) . [ 4 x  y  8  0 ]
2
2. (93/14 O) Given that the normal to the parabola y  4 x  x2 at the point (3,3) forms a triangle with
both the axes. Find the area of the triangle formed.
[2
1
]
4
1
3. (93/18 O) If line y  x is tangential to the curve y  loga x , find a .
[ ee ]
4. (95/17 O) Given that a line which passes through the origin is tangential to y  x3  3x 2  1 , find
[ 1, 3 ,   1 ,  15  ]
the points of contact.
5. (03/17 O) Find the gradient of the curve x2  xy  y 2  1 at the point 1, 1 .

2
8 
[1]
6. (04/17 O) Find the equation of tangent to the curve 2 x3  2 y 3  9 xy at the point (2,1) . [ 5 x  4 y  6 ]
7. (01/20 O) Given a curve has equation
curve at the point (1,1) .
y
x

 x2 y3  0 . Find the equation of tangent to the
1 y 1 x
[ 7 x  11y 18  0 ]