Question

Alright, so I`m reviewing my old calculus notes and I can do quotient rule and everything, but I`m trying to do first principal stuff again and I`m getting stuck. This is my problem:

Determine the Average Rate of Change from x=2 to x=5 given the function: y = x + 1.
I know the answer is one using the power rule, but I`m attempting to do this using first principals only.

These are my steps:

[f(x+h) - f(x)]/h

([(x + h) + 1] - (x + 1) )/h

h/h
as h -> 0
= 0 .

Answer 1

again? why???

Answer 2

Did you forget that the first principles prove the rules and that you never have to look back at it again?

Answer 3

the rate of change of a line is simply the slope ....

Answer 4

I know that, but I'm going to redo the course soon due to a lack of 90% the first time. Thus I need to go back to the basics :/

Answer 5

f(x) = x + 1

f(a+h) - f(a) a+h+1 -a - 1 h
---------- = ------------ = -- = 1
h h h

Answer 6

since the slope is 1 to begin with

Answer 7

I thought it was as h-> 0?

Answer 8

f(x) = 5x + 1

f(a+h) - f(a) 5a+5h+1 -5a - 1 5h
---------- = ---------------- = -- = 5
h h h

Answer 9

the hs cancel out in the algebra

Answer 10

Oh i see.

Answer 11

I was thinking the constant rule >.<.
Thank you very much!

Answer 12

youre welcome