Applying the First Derivative Test In Exercises 57-62, consider the function on the interval . (a) Find the open intervals on which the function is increasing or decreasing.(b) Apply the First Derivative Test to identify all relative extrema, (c) Use a graphing utility to confirm your results.
To calculate: The interval where the first provided function is increasing or decreasing in the domain .
The function .
The function f said to have a critical point at c if:
For any function that is differentiable in the interval and continuous in the interval , the function can be classified as an increasing or a decreasing function based on the following conditions:
If for the interval , the function is said to be increasing in the interval .
If for the interval , the function is said to be decreasing in the interval .
Differentiate the provided function.
Equate this to zero to obtain the critical points.
These critical points give eight intervals:
Take a test point in the interval and check the sign of the derivative.
The function is decreasing in this interval
To calculate: The relative extrema of the function using the first derivative test.
To graph: The function and find the relative extrema.
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