# If x moves from a to a nearby value a + dx, how do you estimate the corresponding change in the value of a differentiable function ƒ(x)? How do you estimate the relative change? The percentage change? Give an example.

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If x moves from a to a nearby value a + dx, how do you estimate the corresponding change in the value of a differentiable function ƒ(x)? How do you estimate the relative change? The percentage change? Give an example.

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Step 1

First of all, consider a differential function f (x).

Consider two points a and a + dx on x axis.

The point on y axis corresponding to a is f (a) and a + dx is f (a + dx).

Therefore, the change in y is delta y and delta y are equal to f (a + dx) – f (a).

Step 2

Now, to calculate the change in the differential function f (x) consider the y diagram.

Calculate the change in the differential function f (x) from point a to the nearby point a + dx.

Step 3

Again, consider the diagram to calculate the relative change.

To calculate the rel...

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