Question

Find the difference quotient (a). f(x) - f(a) / x-a and for (b). f(x+h) - f(x) / h if f(x) = 2x^2 - x +1

Answer 1

need help on b) ?

Answer 2

yeah :)

Answer 3

plug x+h into f(x) everywhere there's an 'x'

Answer 4

eg.: f(x) = x^4 +2x
f(x+h) = (x+h)^4 +2(x+h)

Answer 5

so 2(x+h)^2 - x(x+h) + 1 - (2x^2 - x + 1) / h ?

Answer 6

2(x+h)^2 - x(x+h) + 1 - (2x^2 - x + 1) / h ?
^-----^ ...?

Answer 7

you have an extra 'x' there...

Answer 8

ahh so when it is just x.. u dont have to reuse the whole term inside the parens?

Answer 9

i see

Answer 10

if it's 'x', simply sub.s in "x+h"

Answer 11

so does it end up being 2(x+h)(x+h)-x-h-2x^2-x?

Answer 12

then expand and simplify.... there will be some terms that cancel...

Answer 13

and you never end up redistributing that 2?

Answer 14

Expand
(x+h)(x+h)

Answer 15

2(x^2+2xh+h^2) - x - h ....

Answer 16

2(x^2+2xh+h^2) -x-h-2x^2+x

Answer 17

2x^2+4xh+2h^2 -x -h -2x^2 +x

Answer 18

lol im gonna run out of eraser :)

Answer 19

4x-2h? final answer?

Answer 20

2h^2 +4xh -h

Answer 21

\[ \frac{ 2h^2 +4xh -h }{ h }\]

Answer 22

h in every term...

Answer 23

so pull out the h?

Answer 24

yes

Answer 25

only in the numerator and divide the demonator?

Answer 26

yes

Answer 27

ok!!! awesome thanks so much!!!

Answer 28

sure:)