Question 916232
{{{f(x) = (1/64)(x-3)^2(x+4)^3 }}}


{{{x=0}}}

{{{f(0) = (1/64)(0-3)^2(0+4)^3 }}}

{{{f(0) = (1/64)(-3)^2(4)^3 }}}

{{{f(0) = (1/64)*9*(64) }}}

{{{f(0) = (1/cross(64))*9*cross(64) }}}

{{{f(0) = 9}}}

point is ({{{ 0 }}},{{{9}}})



{{{x=-1}}}

{{{f(-1) = (1/64)(-1-3)^2(-1+4)^3 }}}

{{{f(-1) = (1/64)(-4)^2(3)^3 }}}

{{{f(-1) = (1/64)*(16)*27 }}}

{{{f(-1) = (1/cross(64)4)*cross(16)*27 }}}

{{{f(-1) = 27/4}}}

{{{f(-1) = 6.75}}}

point is ({{{ -1 }}},{{{6.75}}})



{{{x=1}}}

{{{f(1) = (1/64)(1-3)^2(1+4)^3 }}}

{{{f(1) = (1/64)(-2)^2(5)^3 }}}

{{{f(1) = (1/64)*4*125 }}}

{{{f(1) = (1/cross(64)16)*cross(4)*125 }}}

{{{f(1) = 7.8}}}

point is ({{{ 1 }}},{{{7.8}}})


{{{x=-4}}}

{{{f(-4) = (1/64)(-4-3)^2(-4+4)^3 }}}

{{{f(-4) = (1/64)(-7)^2(0)^3 }}}

{{{f(-4) = (1/64)*(49)*0 }}}

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

point is ({{{ -4 }}},{{{ 0 }}})


{{{x=4}}}

{{{f(4) = (1/64)(4-3)^2(4+4)^3 }}}

{{{f(4) = (1/64)(-1)^2(8)^3 }}}

{{{f(4) = (1/64)*1*512 }}}

{{{f(4) = 512/64 }}}

{{{f(4) = 8}}}

point is ({{{ 4 }}},{{{ 8 }}})


{{{x=-5}}}

{{{f(-5) = (1/64)(-5-3)^2(-5+4)^3 }}}

{{{f(-5) = (1/64)(-8)^2(-1)^3 }}}

{{{f(-5) = (1/64)*(64)*(-1) }}}

{{{f(-5) = (1/cross(64))*cross(64)*(-1) }}}

{{{f(-5) = -1}}}


point is ({{{ -5 }}},{{{-1}}})


{{{x=5}}}

{{{f(5) = (1/64)(5-3)^2(5+4)^3 }}}

{{{f(5) = (1/64)(2)^2(9)^3 }}}

{{{f(5) = (1/64)*(4)*(729) }}}

{{{f(5) = (1/cross(64)16)*cross(4)*(729) }}}

{{{f(5) = 729/16}}}

{{{f(5) = 45.6}}}

point is ({{{ 5 }}},{{{45.6}}})





so, we have points:

({{{ 0 }}},{{{9}}})

({{{ -1 }}},{{{6.75}}})

({{{ 1 }}},{{{7.8}}})

({{{ -4 }}},{{{ 0 }}})

({{{ 4 }}},{{{ 8 }}})

({{{ -5 }}},{{{-1}}})

({{{ 5 }}},{{{45.6}}})


{{{drawing( 600, 600, -10, 10, -10, 55,grid(1),circle(5,45.6,.15),circle(-5,-1,.15),  circle(-4,0,.15),  circle(0,9,.15),  circle(-1,6.75,.15),  circle(1,7.8,.15),  circle(-4,0,.15),  circle(4,8,.15), graph( 600, 600, -10, 10, -10, 55, (1/64)(x-3)^2(x+4)^3)) }}}