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.
If the graph of the cubic polynomial has rotational symmetry
then a maximum point must be rotated to become a minimum and vice
versa so the center of rotation will be the midpoint of the line
joining the maximum and minimum points. If there are no maximum and
minimum points then consider the point of inflexion.
The graph of a function has rotational symmetry about the origin
if and only if $f(-x) = -f(x)$. You can do this question without
calculus if you can find the transformation of coordinates that
removes the quadratic term from the polynomial equation.