# Find Where Increasing/Decreasing f(x)=x-1

Find the derivative.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Set the derivative equal to .
Since , there are no solutions.
No solution
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
There are no values of in the domain of the original problem where the derivative of the function is or undefined.
No critical points found
No points make the derivative equal to or undefined. The interval to check if is increasing or decreasing is .
Substitute any number, such as , from the interval in the derivative to check if the result is negative or positive. If the result is negative, the graph is decreasing on the interval . If the result is positive, the graph is increasing on the interval .
Replace the variable with in the expression.
The final answer is .
The result of substituting into is , which is positive, so the graph is increasing on the interval .
Increasing on since
Increasing over the interval means that the function is always increasing.
Always Increasing
Find Where Increasing/Decreasing f(x)=x-1

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