Question 1139374


Average rate of change is just the slope between the 2 points.


 so, average rate of change on {{{x=-4}}} to {{{x=0}}}  is:

{{{(f(0)-f(-4))/(0-(-4))  }}}

={{{(f(0)-f(-4))/(0+4)}}}

={{{(f(0)-f(-4))/4}}}


now find {{{f(x) =2x^3 }}}when {{{x=0}}}

{{{f(0)=2*0^3=0}}}

find {{{f(x) =2x^3}}} when {{{x=-4}}}

{{{f(-4)=2*(-4)^3=2(-64)=-128}}}

plug it in  {{{(f(0)-f(-4))/4}}}

={{{(0-(-128))/4}}}

={{{128/4}}}

={{{32}}}=> rate of change of {{{f(x) =2x^3}}} from {{{-4}}} to{{{ 0}}}