P1^
5
Exercise(^) 5D
(i) Find the gradient function d
d
y
x
.
(ii) Use your answer from part (i) to find the gradient of the curve at P.
(iii) Use your answer from part (ii), and the fact that the gradient of the curve
at P is the same as that of the tangent at P, to find the equation of the
tangent at P in the form y = mx + c.17 The graph of y = x^2 + (^1) x is shown below. The point marked Q is (1, 2).
(i) Find the gradient function d
d
y
x
.
(ii) Find the gradient of the tangent at Q.
(iii) Show that the equation of the normal to the curve at Q can be written as
x + y = 3.
(iv) At what other points does the normal cut the curve?18 The equation of a curve is yx=
(^32)
.
The tangent and normal to the curve at the point x = 4 intersect the x axis at
A and B respectively.
Calculate the length of AB.
19 (i) The diagram shows the line 2y = x + 5 and the curve y = x^2 – 4x + 7,
which intersect at the points A and B.
x
y
O
Q
x
y
O
A
B
2 y = x + 5
y = x^2 – 4x + 7