The First Derivative Test for Relative Maximum and Minimum - Concept

Concept Concept (1)

The first derivative test is a way to find if a critical point of a continuous function is a relative minimum or maximum. Simply, if the first derivative is negative to the left of the critical point, and positive to the right of it, it is a relative minimum. If the first derivative test finds the first derivative is positive to the left of the critical point, and negative to the right of it, the critical point is a relative maximum.

Sample Sample Problems (3)

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The First Derivative Test for Relative Maximum and Minimum - Problem 1
Problem 1
How to use the first derivative test to identify what critical points are relative maxima and minima for the function, f(x) = x^3 - 6x^2 - 63x + 42.
The First Derivative Test for Relative Maximum and Minimum - Problem 2
Problem 2
How to use the first derivative test to find a which critical points of a function, f(x) = x (5-x)^(2/3), are relative maxima and minima.
The First Derivative Test for Relative Maximum and Minimum - Problem 3
Problem 3
How to use the first derivative test to identify a rational function's relative maxima and minima