Question 1196097


if

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

find:

{{{(f(7 + h) -f(7))/ h}}} , {{{h}}} ≠ {{{0}}}


first find {{{f(7 + h)  }}}

{{{f(7 + h) = (7 + h)^2 - 2(7 + h)+ 4}}} 

{{{f(7 + h) = h^2 + 14h + 49- 14 -2h+ 4 }}}

{{{f(7 + h) = h^2 + 12 h + 39}}}


now find {{{f(7)}}}

{{{f(7) = 7^2 - 2*7 + 4 =39}}}


then 

{{{(f(7 + h) -f(7))/ h =(h^2 + 12 h + 39 -39)/ h }}}

{{{(f(7 + h) -f(7))/ h =(h^2 + 12h )/ h }}}

{{{(f(7 + h) -f(7))/ h =h(h + 12 )/ h }}}

{{{(f(7 + h) -f(7))/ h =h + 12 }}}