Question

A polynomial function $P ( x )$ of degree 5 with leading coefficient one, increases in the interval $(-\infty, 1)$ and $(3, \infty)$ and decreases in the interval $(1,3)$. Given that $P(0)=4$ and $P^{\prime}(2)=0$. Find the value $P^{\prime}(6)$.

Answer 1

$\because $ Degree of $P ( x )$ is 5 with leading coefficient one.
$\therefore \text { degree of } P ^{\prime}( x ) \text { is } 4 \text { with leading coefficient five. } $
$\therefore P ^{\prime}( x )=5( x -1)( x -3)( x -2)^2$
$\therefore P ^{\prime}(6)=5 \times 5 \times 3 \times 4^2$
$ =1200$