Over what interval is the function increasing, and over what interval is the function decreasing?
The function f(x) is increasing over the interval
(Simplify your answer. Type an inequality.)
Analyzing Intervals of Increase and Decrease for the Function f(x)
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To determine where the function ( f(x) ) is increasing or decreasing, you’ll need to find the first derivative ( f'(x) ). The function is increasing where ( f'(x) > 0 ) and decreasing where ( f'(x) < 0 ).
1. Find the Derivative: Compute ( f'(x) ).
2. Set the Derivative to Zero: Solve ( f'(x) = 0 ) to find critical points.
3. Analyze the Sign: Test intervals between the critical points to see where ( f'(x) ) is positive (increasing) and where it is negative (decreasing).
Once you have done these steps, you can write the intervals in inequality form.
If you have the specific function or further details, feel free to share for more tailored assistance!
To determine where the function ( f(x) ) is increasing or decreasing, you first need to find its derivative, ( f'(x) ). The function is increasing where ( f'(x) > 0 ) and decreasing where ( f'(x) < 0 ).
1. Find the derivative: Differentiate ( f(x) ) to find ( f'(x) ).
2. Set the derivative to zero: Find the critical points by solving ( f'(x) = 0 ).
3. Test intervals: Choose test points in each interval determined by the critical points to see if ( f'(x) ) is positive or negative.
Once you identify the intervals where ( f'(x) > 0 ) (increasing) and ( f'(x) < 0 ) (decreasing), you can write your answer in inequality form.
Please provide the function ( f(x) ) so I can help you with the specific intervals!