17.1. Increments
If two points ( x1, y1 ) and ( x2, y2 ) lie on the graph of f(x), the increment in x ( Δx ) is the difference between x2 and x1. Similarly, the increment in y ( Δy ) is the different between y2 and y1.
Therefore x2 can also be defined as x1 plus Δx. Thus Δy can also be defined as:
Illustrative Example
Let f(x) = x^2 - x + 2. If x jumps from 3 to 3.2, what is Δy?
Solution
Solution
Calculator solution
Step 1: Enter x1 = 3 by tapping x, 1, =, 3 in order.
Step 2: Enter x2 = 3.2 by tapping x, 2, = , 3.2 in order.
Step 3: Type in the given function f(x) = x^2 - x + 2 by doing the following:
Go to the a-z keyboard to type the letter f
Then switch back to the 0-9 keyboard and continue entering the equation: f(x) = x^2 - x + 2
Step 4: Enter the formula for Δy by doing the following:
Go to the a-z keyboard to type the letter f
Then switch back to the 0-9 keyboard and continue typing: f( x2 ) - f( x1 )
Step 1: Enter x1 = 3 by tapping x, 1, =, 3 in order.
Step 2: Enter x2 = 3.2 by tapping x, 2, = , 3.2 in order.
Step 3: Type in the given function f(x) = x^2 - x + 2 by doing the following:
Go to the a-z keyboard to type the letter f
Then switch back to the 0-9 keyboard and continue entering the equation: f(x) = x^2 - x + 2
Step 4: Enter the formula for Δy by doing the following:
Go to the a-z keyboard to type the letter f
Then switch back to the 0-9 keyboard and continue typing: f( x2 ) - f( x1 )
Refer to the screenshot below.