Plot points with coordinates where \(x\) and \(y\) are equal. Three points are sufficient, but more can be plotted. Draw a line through the plotted points. If \(x\) is positive, \(y\) is negative. If ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

Give an example of a function with one critical point which is also an inflection point. You must provide the equation of your function. A particle moves along a line with a position function \(s(t)\) ...

Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...