SOLUTION: Q: Let f(x) = {{{ (3x-1)/(x+2) }}} Find f ' (x) first set up the limits & simplify My soltn: lim x->c {{{ (f(x)-f(c))/(x-c) }}} lim x->c {{{ (((3x-1)/(x+2))-((3c-1)/(c+2)))

Question 991172: Q: Let f(x) =
Find f ' (x) first set up the limits & simplify
My soltn:
lim x->c
lim x->c
I got the solution 7/(x+2)(c+2) but my program keeps saying this is incorrect.
Please help!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
f'(x) = limit as h --> 0 of ( f(x+h) - f(x) ) / h
*******************************************************************
we are given the function,
f(x) = (3x-1) / (x+2)
*******************************************************************
f'(x) = limit as h --> 0 of (( 3(x+h)-1 / (x+h+2) ) - ( (3x-1) / (x+2) )) / h =
( 3x+3h-1 ) / (x+h+2) ) - ( (3x-1) / (x+2) ) / h =
( (x+2)*(3x+3h-1) - ( (x+h+2)*(3x-1) ) / (x+h+2)*(xh+2h) =
( (3x^2+3hx+5x+6h-2) - (3x^2+3hx+5x-h-2) ) / (x^2h+xh^2+4xh+2h^2+4h) =
( 7h ) / (x^2h+xh^2+4xh+2h^2+4h) =
7 / (x^2 +xh +4x +2h + 4) =
as h -->0 xh and 2h terms go to 0, then we have
7 / (x^2 +4x + 4) =
7 / (x+2)^2

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