Question 1005325
The function is {{{y=x^2 +3x}}} .
The secant requested is the straight line that passes through points
{{{A}}} with {{{system(x[A]=3,y[A]=3^2+3*3=9+9=18)}}} and
{{{B}}} with {{{system(x[B]=3+h,y[B]=(3+h)^2^2+3(3+h)=9+6h+h^2+9+3h=18+9h+h^2)}}}
The slope of secant {{{AB}}} is
{{{m=(y[B]-y[A])/(x[B]-x[A])}}} --> {{{m=(18+9h+h^2-18)/(3+h-3)}}} --> {{{m=(9h+h^2)/h}}} --> {{{m=h(9+h)/h}}} --> {{{highlight(m=9+h)}}}


The graph with the secants for h=1, h=2, and h=3 are shown below.
{{{graph(900,600,-1,7,-5,55,x^2+3x,12(x-3)+18,11(x-3)+18,10(x-3)+18)}}}