Question 1196945
to determine the zeros of the {{{f(x)=x^2-3x-4}}}, set {{{f(x)=0}}}


{{{0=x^2-3x-4}}}...........factor

{{{0=x^2+x-4x-4}}}

{{{0=(x^2+x)-(4x+4)}}}

{{{0=x(x+1)-4(x+1)}}}

{{{0 = (x - 4)(x + 1)}}}

solutions:

if {{{0 = (x - 4)}}} =>{{{x=4}}}

if {{{0 = (x + 1)}}}=>{{{x=-1}}}

so, zeros are {{{-1}}} and {{{4}}}



{{{ graph( 600, 600, -10, 10, -10, 10, x^2-3x-4) }}}



the instantaneous rate of change in {{{f(x)}}} at the zeros:


∆y/∆x={{{(f(x2) -f(x1) )/(x2 - x1 )}}}

∆y/∆x={{{(f(4) -f(-1) )/(4 - 1 )}}}

∆y/∆x={{{(f(4) -f(-1) )/3}}}

find {{{f(4)}}} and {{{f(-1)}}}

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

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


then

∆y/∆x={{{(0 -0 )/3=0/3=0}}}