sorry to ask for so much help
they ask me to find the average rate of change from x=1 to x=2 in the equation x-2x^2
then they give me the equation x^2-2 and ask me to find f(x+h)-f(x)/h
thank you.
Hello, jhonwashington!
. . . . . . . . . . . . . . . . . . . . . . . . . change in f(x)Find the average rate of the function: .f(x) .= .x - 2x² from x=1 to x=2.
Average rate of change of f(x) . = . -----------------
. . . . . . . . . . . . . . . . . . . . . . . . . .change in x
We have: . f(1) .= .1 - 2(1²) .= .-1
. . . .and: . f(2) .= .2 - 2(2²) .= .-6
The change in f(x) is: .(-6) - (-1) .= .-5
The change in x is: .2 - 1 .= .1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -5
Therefore, average rate of change of f(x): . -- . = . -5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Given: .f(x) .= .x² - 2
. . . . f(x + h) - f(x)
Find -----------------
. . . . . . . . h
There are three steps to this "difference quotient":
. . (1) Find f(x + h) ... and simplify
. . (2) Subtract f(x) ... and simplify
. . (3) Divide by h ... and simplify
We have:
(1) f(x+h) .= .(x+h)² - 2 .= .x² + 2xh + h² - 2
(2) f(x+h) - f(x) .= .(x² + 2xh + h² - 2) - (x² - 2) .= .2xh + h²
. . .f(x+h) - f(x) . . .2xh + h² . . h(2x + h)
(3) -------------- .= .---------- .= .----------- .= .2x + h
. . . . . . h . . . . . . . . . h . . . . . . . .h