What is the difference between 1st and 2nd derivative test?
?
2012-03-26 17:54:48 UTC
I'm learning about how to find the relative maximum and minimum using the 1st derivative test, and the 2nd derivative test. I keep getting confused about how they are different? Can someone please explain exactly how ? Thanks!!!
Four answers:
2012-03-26 17:58:36 UTC
The first derivative represents the slope of the function at any given point. So local maximums and local minimums will be located where the first derivative = 0.
The second derivative measures the rate of change of the slope. When the second derivative = 0 this represents the inflection point. This is where the function changes from being concave to convex or vice versa.
To find all local max and mins first find the first derivative. Set the first derivative equal to 0 and solve. The values you get will represent local mins or maximums. To test whether they are max or mins you must take the second derivative. If the second derivative is positive at the point where there is the critical point then it is a local minimum. If the second derivative is negative then it is a local maximum.
2012-03-26 18:01:12 UTC
The first derivative test is showing the slope of the f (x) function, it is used to find where the slope is zero, or a local max or min where the graph turns around.
The second derivative test is kind of tricky, it shows where the slope changes from increasing to decreasing or vise versa, or points of concavity, in motion it is used to find where the velocity of an object is increasing or decreasing. If the slope is increasing, it is called concave upward, this is where your second derivative is > 0, if the slop is decreasing it is concave downward or < 0. don't let the looks of the graph fool you, just because the slope is positive doesn't mean it's not decreasing
?
2016-11-07 10:29:38 UTC
1st Derivative
hamiton
2016-11-29 16:18:03 UTC
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