If $y=f(x)$ has a turning point when $x=\frac{1}{4}$, can we find $\lambda$?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

It is given that \[f(x)=(x-2)^2-\lambda(x+1)(x+2).\]

1. Find the values of \(\lambda\) for which the equation \(f(x)=0\) has two equal roots.

2. Show that, when \(\lambda=2\), \(f(x)\) has a maximum value of \(25\).

3. Given that the curve \(y=f(x)\) has a turning point when \(x=\dfrac{1}{4}\), find the value of \(\lambda\) and sketch the curve for this value of \(\lambda\).