1 Write the equation of the line through (3.2) and (1,10), preferably in the ax+by=c form.
2 Write the equation of the line perpendicular to 2x + 3y = 16 that passes through (-1,2).
3 Write the equation of the circle with centre (2,3) and radius 5.
4 Show that x2 + 8x + y2 – 6y = 24 is a circle by finding its centre and radius.
5 Identify and classify the stationary values of y = 2x5 + 5x4 – 10x3 .
6 The curve y = (x - 3) (x + 1) has a tangent at x = 2. Find the equation of this line and state its intercepts.
7 Sketch the line in Question 5, showing intercepts and stationary values.
8 Attempt a sketch of the line y = (x + 3) .
(x + 2)(x - 1)
Differentiation Practice
1 d (x3 + 5x2)
dx
2 d (x-2 + 2x-1)
dx
3 d (5 √t – 1/t)
dt
4 d (y3)
dt
5 d (x2 + 5)4
dx
6 d (3x4 + 6)2
dx
7 d (x y)
dt
8 d (3x2 + 1)( x3 - 3)
dx
9 d (1 + x + x2/2 + x3/6 + x4 /24)
dx
10Where is the maximum of
y = 2x3 – 6x2 + 7 ?
This exercise is graduated through the chain rule and the product rule. Revise as necessary.