If x, y and z are real numbers such that: x + y + z = 5 and xy + yz
+ zx = 3. What is the largest value that any of the numbers can
Knowing two of the equations find the equations of the 12 graphs of
cubic functions making this pattern.
Find the relationship between the locations of points of inflection, maxima and minima of functions.
Prove that the graph of the polynomial
$f(x) = x^3 - 6x^2 +9x +1$
has rotational symmetry, find the centre of rotation and
re-write the equation of the graph in terms of new co-ordinates
$(u,v)$ with the origin of the new co-ordinate system at the centre
Do the same for the graph of the function $g(x) =
2x^3 + 3x^2 +5x +4$ .
Prove that the graphs of all cubic polynomials have rotational