Consider the curve with the equation \(f(x) = px^2 +qx\), wher \(p\) and \(q\) are constants. The point \(\mathrm{A}(1,3)\) lies on the curve. The tangent to the curve at \(\mathrm{A}\) has gradient \(8\). Find the value of \(p\) and of \(q\).[7]

Consider the curve with the equation \(f(x) = px^2 +qx\), wher \(p\) and \(q\) are constants. The point \(\mathrm{A}(1,3)\) lies on the curve. The tangent to the curve at \(\mathrm{A}\) has gradient \(8\).
Find the value of \(p\) and of \(q\).

Differentiation Techniques

International Baccalaureate Standard Level Mathematics