3
Given that y (i) (ii)
4
(ii) (iii) (iv)
5
find dy dx find any stationary points and determine their nature sketch the curve.
Given that y (i)
2)2
1)(x
x x
3 4
find dy dx find the equation of the tangent to the curve at the point (6, 1.5) find the equation of the normal to the curve at the point (5, 2) use your answer from part (i) to deduce that the curve has no stationary points, and sketch the graph. 2x
The diagram shows the graph of y = x
x −1
P2 4 Exercise 4A
(iii)
(x
, which is undefined for x < 0 and
1. P is a minimum point. y
P
x
(i) (ii) (iii) (iv) (v)
(vi)
Find dy . dx Find the gradient of the curve at (9, 9), and show that the equation of the normal at (9, 9) is y 4x 45. Find the co-ordinates of P and verify that it is a minimum point. Write down the equation of the tangent and the normal to the curve at P. Write down the point of intersection of the normal found in part (ii) and (a) the tangent found in part (iv), call it Q (b) the normal found in part (iv), call it R. Show that the area of the triangle PQR is 441 . 8
83