Give an example of a function with one critical point which is also an inflection point. You must provide the equation of your function. Give an example of a function that satisfies \(f(-1)=f(1)=0\) ...

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).

Below is the graph of a quadratic function, showing where the function is increasing and decreasing. If we draw in the tangents to the curve, you will notice that if the gradient of the tangent is ...