91Ó°ÊÓ

The given function is:$f\left(x\right)={\left(x+2\right)}^a{x}^b{\left(x-2\right)}^c$

While $c=1$the graph for given function looks like as follows:

The graph of the function f intersects the x axis at $x=2$when $c=1$

.(Because the multiplicity of the zero point is $1$(the number is odd), the graph of the function f overlaps the x axis.)

While $c=2$, The graph for given functions looks like as follows:

The graph of the function f touches the x axis at$x=2$when$c=2$.We claim that the local minimum is obtained at $x=2$because the graph of the function f meets the x axis since the multiplicity of the zero point equals $2$(even number).

While $c=3$, The graph for given functions looks like as follows:

The graph of the function f intersects the x axis at $x=2$when $c=3$. (We say the graph of the function f flattens more at the zero point because it intersects the x axis.) It's not the same as when c was $1$. Because the zero point's multiplicity is $3$(an odd number), the graph of the function f contacts the x axis and flattens out towards the zero point.