how to find difference quotient for:
f(x) = 1/x+3
So I am reading that as f(x)=(1/x) + 3
difference= f(x+e)-f(x)=1/(x+e) + 3 - 1/x -3= (x-x-e)/((x+e)(x))
difference quotent=difference/e= (- 1)/(x^2 +xe ) =
or, see your previous post of 1:48 pm
To find the difference quotient of a function, you need to calculate the average rate of change of the function as the distance between the two points on the graph approaches zero. The formula for the difference quotient is:
[f(x + h) - f(x)] / h
where h represents a small change or difference in the value of x.
To find the difference quotient for the function f(x) = 1/(x + 3), follow these steps:
Step 1: Replace f(x) in the difference quotient formula with the given function, 1/(x + 3):
[f(x + h) - f(x)] / h = [1/((x + h) + 3) - 1/(x + 3)] / h
Step 2: Simplify the expression inside the brackets. To do this, we need to find a common denominator:
[f(x + h) - f(x)] / h = [(x + 3) - (x + h + 3)] / [(x + h + 3)(x + 3)]
Step 3: Expand and simplify the numerator:
[f(x + h) - f(x)] / h = [x + 3 - x - h - 3] / [(x + h + 3)(x + 3)]
The x terms and the 3 terms will cancel each other out, leaving:
[f(x + h) - f(x)] / h = -h / [(x + h + 3)(x + 3)]
Step 4: Simplify the denominator by expanding it:
[f(x + h) - f(x)] / h = -h / (x^2 + (4h + 6)x + 3h + 9)
So, the difference quotient for the function f(x) = 1/(x + 3) is -h / (x^2 + (4h + 6)x + 3h + 9).