Question

Let $f\left(x\right)={(x-2)}^{33}{(x-3)}^{44}$ then which of the following is true

• A. $x=2$ is point of inflexion
• B. $x=3$ is point of minima
• C. $x=\frac{17}{7}$ is point of maxima
• D. All of these

Answer 1

The correct option is D All of these

From the equation we can easily tell that
$x=2$ is a point of inflection.
Now
$f^{\prime }\left(x\right)=33(x-2{)}^{32}.(x-3{)}^{44}+44(x-{)}^{43}.(x-2{)}^{33}$
$=(x-2{)}^{32}(x-3{)}^{43}\left[33\right(x-3)+44(x-2\left)\right]$
$=(x-2{)}^{32}(x-3{)}^{43}[77x-99-88]=0$
Or
$77x-187=0$
$x=\frac{187}{77}$
$=\frac{17}{7}$.
Hence
$x=\frac{17}{7}$ is point of maxima.