Why is it called f(x+Δx)?

iamaditya · 2017-08-22 07:08:24

I was learning differential calculus from mif when I saw this:

Why is the above point called f(x+Δx)?

zetafunc · 2017-08-22 08:50:38

The first point is . The second point is .

Bob · 2017-08-22 19:32:16

hi iamaditya

In differential calculus, we are trying to develop a rule for how the gradient of a function varies with x. The usual method for working this out is this:

(1) Pick a point on the curve for the function, say ( x, f(x) )

(2) Move to a point close to ( x, f(x) ). The way this is written is ( x + Δx, f(x+Δx) ) meaning ("x plus a little bit more in the x direction", "value of the function at this new value of x")

note: Δx should be regarded as a single variable, not as two variables multiplied together. Thus Δy/Δx must not be simplified to y/x by cancelling! This should be considered as "a little bit in the y direction"/"a little bit in the x direction"

(3) The gradient of the chord joining these points is then considered, simplifying where possible.

(4) Then Δx is reduced towards zero, to see if the gradient found in step (3) tends towards a recognisable gradient function.

(5) This gradient function is usually written dy/dx. Again these two, dy and dx, should be treated as two single variables so the 'd's cannot be cancelled.

Some texts avoid this confusion by using x + h and f(x+h) where 'h' is a small amount in the x direction.

eg https://diversity.umn.edu/multicultural … nRules.pdf

Hope that helps,

Bob

iamaditya · 2017-08-22 22:21:23

Thnx bob and zetafunc.

Math Is Fun Forum

#1 2017-08-22 07:08:24

Why is it called f(x+Δx)?

#2 2017-08-22 08:50:38

Re: Why is it called f(x+Δx)?

#3 2017-08-22 19:32:16

Re: Why is it called f(x+Δx)?

#4 2017-08-22 22:21:23

Re: Why is it called f(x+Δx)?

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