Question 1127529

 {{{f(x)=-x^3+3x^2 }}} from {{{x=-1}}} to {{{x=4 }}}

average rate of change is simply the slope of the line through ({{{-1}}},{{{f(-1)}}}) and ({{{4}}},{{{f(4)}}})

{{{f(-1)=-(-1)^3+3(-1)^2}}}
{{{f(-1)=1+3}}}
{{{f(-1)=4}}}

{{{f(4)=-(4)^3+3(4)^2}}}
{{{f(4)=-64+48}}}
{{{f(4)=-16}}}

so, the points are ({{{-1}}},{{{4}}}) and ({{{4}}},{{{-16}}})

average rate of change is: 

{{{(-16-4)/(4-(-1))=-20/5=-4}}}