Review question

# 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

Ref: R7998

## Question

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 $\lambda$.