Question

Simplify the difference quotient
[f(2 + h) − f(2)]/h ; if h ≠ 0.

f(x) = x2 − 3x

I keep getting the answer wrong. I must be messing up my steps...Please Help

Answer 1

f (2 + h ) = ( 2 + h ) ^ 2 - 3 * ( 2 + h )

f ( 2 ) = 2 ^ 2 - 3 * 2 = 4 - 6 = - 2


[ f ( 2 + h ) − f ( 2 ) ] / h =

[ ( 2 + h ) ^ 2 - 3 * ( 2 + h ) - ( - 2 ) ] =

[ 2 ^ 2 + 2 * 2 * h + h ^ 2 - 3 * 2 - 3 * h + 2 ] / h =

[ 4 + 4 h + h ^ 2 - 6 - 3 h + 2 ] / h =

( h ^ 2 + h ) / h = h * ( h + 1 ) / h = h + 1

Answer 2

[ f ( 2 + h ) − f ( 2 ) ] / h =

[ ( 2 + h ) ^ 2 - 3 * ( 2 + h ) - ( - 2 ) ] / h =

[ 2 ^ 2 + 2 * 2 * h + h ^ 2 - 3 * 2 - 3 * h + 2 ] / h =

[ 4 + 4 h + h ^ 2 - 6 - 3 h + 2 ] / h =

( h ^ 2 + h ) / h = h * ( h + 1 ) / h = h + 1

Answer 3

OH! thanks. I just messed up a tiny calculation haha. It's such a messy question..