Graph sketching

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Can you massage the parameters of these curves to make them match as closely as possible?

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

Can you sketch these difficult curves, which have uses in mathematical modelling?