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/dx (x3 + 5x2)
2 d/dx (x-2 + 2x-1)
3 d/dt (5 √t – 1/t)
4 d/dt (y3)
5 d/dx (x2 + 5)4
6 d/dx (3x4 + 6)2
7 d/dt (x . y)
8 d/dx (3x2 + 1)( x3 - 3)
9 d/dx (1 + x + x2/2 + x3/6 + x4 /24)
10 Where is the maximum of y = 2x3 – 6x2 + 7 ?
This exercise is graduated through the chain rule and the product rule.
Revise as necessary. Be careful with the w.r.t. element (the x in d/dx ).
Index often fails to display as superscript. It varies with the software and particularly with transfers between software packages.
