Therefore, aim to recognise the equations and graphs of quadratics, cubics, reciprocals, exponentials and circles. Sketch \(y = x^2 + x − 6\). The quadratic factorises to give \((x + 3)(x − 2 ...

This type of curve is called a parabola and it is symmetrical. To draw the graph we need coordinates. We generate these coordinates by substituting values into the quadratic equation. A quadratic ...

Find all intervals on which \(f\) is concave up and those on which \(f\) is concave down. Find the \((x,y)\) coordinates of all inflection points, if any. Sketch the graph of \(y=f(x)\) using all of ...

is decreasing. If \(f\) is a polynomial function, what is the least possible degree of \(f\text{?}\) Figure 3.2.2. The graph of \(\ds f^\prime(x)\) Sketch the graph of \(f(x)=3x^4-8x^3+10\text{,}\) ...