Question 977422


{{{f(x)=-x^4+4x^3-2x^2+x+1}}}, from {{{x}}}:{{{0}}} to {{{x}}}:{{{1}}}

{{{f(x)=-x^4+4x^3-2x^2+x+1}}}, if {{{x=0}}}

{{{f(0)=-0^4+4*0^3-2*0^2+0+1=1}}}

so, point is ({{{x}}},{{{f(0)}}})=({{{0}}},{{{0}}})


if {{{x=1}}}
{{{f(1)=-1^4+4*1^3-2*1^2+1+1}}}, 

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

{{{f(1)=3}}}

so, point is ({{{x}}},{{{f(1)}}})=({{{1}}},{{{3}}})


average rate of change, or slope is:

{{{(f(1)-f(0)) /(1-0) = (3-1)/1 = 2}}}