Question 1182973

In order for it to be positive before and negative after {{{x=2}}}, then it must look like this,
{{{f(x)=a(x-2)^3}}}
or else you will have an additional set of directional changes.
So now solve for the constant.
After {{{x=2 }}}the cubic will be positive so the constant needs to be negative.

So,

{{{f(x)=-a(x-2)^3}}}

{{{f(0)=-a(0-2)^3=4}}}

{{{a=4/8}}}

{{{a=1/2}}}



{{{f(x)=-(1/2)(x-2)^3}}}


{{{ graph( 600, 600, -10, 10, -10, 10, -(1/2)(x-2)^3) }}}