PROPERTIES OF CURVES (Chapter 13)
340
ACTIVITY
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REVIEW SET 13A
b y = x - 5x + 2 at (2,0)
1 Find the equation of the tangent to:
a y=-222 at the point where x = -1
1-2x
at (1, -
d f(x) = (3x-1
at the point where 1 =
e f(x) = ln(x-2) at the point where x = e.
2 Find the equation of the normal to:
a y = 13.1 +4 at (4,4)
y = 3e2:
a
Find a.
b
at the point where I = 1.
3 At the point where x = 0, the tangent to f(x) = 4x + px + q has equation y = 50-1
Find p and q.
4 Find all points on the curve y = 22 + 3.22 - 10x +3 where the gradient of the tangent is 2
5 The line through A(2, 4) and B(0,8) is a tangent to y=
(x + 2)2
6 Find where the tangent to y = 228 +4x – 1 at (1,5) meets the curve again.
a Find the equation of the normal to y = e2c at the point where x = a.
b Hence find the equation of the normal to y = e21 which passes through the origin.
8 Find the coordinates of P and Q if (PQ)
5
y =
at (1,5).
va
7
YA
is the tangent to
P
(1,5)
5
y =
Q
The tangent to y = x+/T = c at * = -3 cuts the axes at points A and B.
Determine the area of triangle OAB.
Find intervals where f(x) = -23 - 6x2 + 36x - 17 is:
a increasing
Consider the function f(x) = 2x3 - 3x2 - 360 +7.
a Find and classify all stationary points.
b decreasing
b Find intervals where the function is increasing and decreasing.
Describe the behaviour of the function as 200 and as X-→ -0.
d Sketch the graph of y=f(x) showing the
