First Derivative Test Describe the First Derivative Test in your own words.
The First derivative test.
A function .
The first derivative test is used to determine the relative extremes of a function with the help of the first order differential.
A number in the domain is said to be the critical point of a function if the value of the first derivative at that point is zero.
So, for a critical point c of a function , the following applies:
If the derivative of the function, changes sign from a negative value to a positive value at the point c, then f is said to have a relative minima at the point c.
If the derivative of the function, changes sign from a positive value to a negative value at the point c, then f is said to have a relative maxima at the point c.
If the derivative function does not change sign at the critical point, the point is neither a maxima nor a minima.
Consider the following function:
Differentiate both sides with respect to x and equate the differential to zero to obtain the critical points,
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