Help answering this?

Question

Consider the function  and find the following:

c) The average rate of change between the points (x,f(x)) and (x+h,f(x+h))

I've gotten h as my answer twice, but that doesn't seem to be right.

 .

Answer 1

The average rate of change is just looking at the change between the rise and the run or the slope of the function. Which can be calculated using the slope formula.

y2-y1 f(x+h) - f(x)

——- = —————

x2-x1 (x+h)- x

which then simplifies to

f(x+h) - f(x)

—————

h

you actually can’t simplify the f(x) in the numerator because a function does not distribute through to the x and the h separately. You could not simplify the numerator unless you knew the function f(x).

Answer 2

Garrett. Rate of change = change in y / change in x, so [ f(x+h) - f(x) ] / h.

Can't be simplified further than this, unless f(x) is defined.

Mike