Question 1170598
given:

the gradient of the curve: {{{dy/dx= 2x^2 - 5x}}}
 the point ({{{3}}},{{{ 8}}})

since gradient is function degree{{{ 2}}}, we are looking for function degree {{{3}}}

{{{f(x)=ax^3+bx^2+cx }}}

{{{dy/dx= 2x^2 - 5x}}} ... integrating this we get, .......{{{3*(1/a)=2}}}->{{{a=2/3}}}, and {{{2*(1/b)=5}}}->{{{b=5/2}}}

{{{f(x)= (2/3)x^3 - (5/2)x^2+c}}}  .......use given point ({{{3}}}, {{{8}}}) to calculate {{{c}}}

{{{8= (2/3)3^3 - (5/2)3^2+c }}}

{{{8= 18 - 45/2+c }}}

{{{c=8-18+45/2}}}

{{{c= 25/2}}}


{{{f(x)= (2/3)x^3 - (5/2)x^2+25/2}}}


{{{drawing( 600, 600, -10, 20, -10, 20,
circle(3,8,.12),locate(3,8,p(3,8)),
 graph( 600, 600, -10, 20, -10, 20,(2/3)x^3 - (5/2)x^2+25/2)) }}}