Posts Tagged ‘decreasing’
Thursday, October 8th, 2009
How to Use the First Derivative Test
Description
A detailed tutorial on how to use the first derivative test. Step by step tutorial including several examples of how to use the first derivative test for reference.
Overview
The first derivative test involves taking the derivative of a function that you would like to find the local maximum or minimum of. Once you have the derivative, you must determine if the function is increasing or decreasing. If the derivative is positive, the function is increasing, and when the derivative is negative, the function is decreasing. If the derivative cannot be determined as positive or negative, then the test fails.
Tags: Calculus, chart, critical points, decreasing, derivative, extrema, extremum, first derivative test, function, graph, increasing, Math, maxima, maximum, minima, minimum, negative, positive, second derivative test
Posted in Calculus | No Comments »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Alternating Series Test
Description
A detailed tutorial on testing for convergence using the alternating series test. Step by step tutorial including several examples of testing for convergence using the alternating series test for reference.
Overview
The alternating series test, like all convergence and divergence tests, is fairly easy. The hardest part is figuring out if you should use the AST, or a different test. An easy way to tell is, is the equation negative? What would happen if you pulled a negative one out? Or maybe, there is already a negative one outside of the equation. If you see any fraction, function, or any equation at all with a -1 to an odd power at the front (or at the front of the numerator, in a fraction) then you should use the alternating series test for it. If the series is decreasing over time, and the limit is approaching zero, then the series is convergent. The alternating series test is normally used in conjunction with another test for convergence.
Tags: -1, alternating, AST, Calculus, converge, convergence, decreasing, diverge, divergence, fraction, function, limit, Math, negative, one, series, test, zero
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
Explanation of the Monotonicity Theorem
Description
A detailed tutorial on the solving of the Monotonicity Theorem. Step by step tutorial including several examples of how to solve the Monotonicity Theorem for reference.
Overview
The Monotonicity Theorem is used to determine if a function is increasing or decreasing. The Monotonicity Theoream states that:
If f ‘(x) > 0 the function is increasing
If f ‘(x) < 0 the function is decreasing
This is basically a repeat of information you already know. The derivative is the same as the slope of a line, and it is obvious to anyone who has spent time studying grpahs that a positive slope increases and a negative slope descreases. Simply find your function, take a derivative, and set it to either less than or greater than 0 to figure out if your graph will be increasing or decreasing.
Tags: 0, Calculus, decreasing, derivative, function, greater than, increasing, less than, Math, monotonicity, monotonicity theorem, slope, zero
Posted in Calculus | No Comments »
