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How can you find the intervals in which the mathematical functions are strictly increasing or decreasing?
Wiki User
∙ 12y ago
You take the derivative of the function, then solve the inequality:
- derivative > 0 for increasing, or
- derivative < 0 for decreasing.
Wiki User
∙ 12y ago
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If the derivative of a function equals xsquared - 2divided byx on which intervals is f decreasing?
f(x) is decreasing on the interval on which f'(x) is negative. So we want: (x2-2)/x<0 For this to be true either the numerator or the denominator (but not both) must be negative. On the interval x>0, the numerator is negative for 0<x<sqrt(2) and the denominator is positive for all x>0. On the interval x<0, the denominator is negative for all values on this interval. The numerator is positive on this interval for x<-sqrt(2). So, f' is negative (and f is decreasing) on the intervals: (-infinity, -sqrt(2)), (0, sqrt(2))
What are the disadvantages of a stem and leaf diagram?
The major disadvantage of the Stem and Leaf plot is that it is dependant on the choice of intervals. The plot is not unique.
How do you identify the range of a function?
The range of a function is the interval (or intervals) over which the independent variable is valid, i.e. results in a valid value of the function.
What is the absolute value of 99-96?
195
What are the intervals over which the function is increasing or decreasing?
It depends on the function.
What function family has an increasing interval and a decreasing interval?
There are many families of functions or function types that have both increasing and decreasing intervals. One example is the parabolic functions (and functions of even powers), such as f(x)=x^2 or f(x)=x^4. Namely, f(x) = x^n, where n is an element of even natural numbers. If we let f(x) = x^2, then f'(x)=2x, which is < 0 (i.e. f(x) is decreasing) when x<0, and f'(x) > 0 (i.e. f(x) is increasing), when x > 0. Another example are trigonometric functions, such as f(x) = sin(x). Finding the derivative (i.e. f'(x) = cos(x)) and critical points will show this.
How do you figure out the intervals of increasing and decreasing of the function y equals x divided by square root of x squared then plus one?
The intervals are determined by when the derivative is positive or negative, because the derivative is the slope and a negative slope means the function is decreasing. The function y=(x/sqrt(x2))+1, however, can be rewritten as y=x/absolutevalue(x) + 1, and as such will be represented as a pair of parallel lines, y=0 for x<0 and y=2 for x>0. As the lines are horizontal, the function is never increasing or decreasing.
Which Greek philosopher discovered the mathematical ratios of musical intervals?
Pythagoras
How do you determine the relative minimum and relative maximum values of functions and the intervals on which functions are decreasing or increasing?
You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.
What are good heart healthy exercise tips?
Intervals are one of the best exercises in strengthening your heart. Intervals puts healthy stress on your heart increasing blood flow and overall health.
When you are comparing equal intervals of time how does the distance change?
The answer depends on whether it is uniform motion, motion under constant acceleration, motion under constantly increasing (decreasing) acceleration, or something else. Since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer. The answer depends on whether it is uniform motion, motion under constant acceleration, motion under constantly increasing (decreasing) acceleration, or something else. Since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer. The answer depends on whether it is uniform motion, motion under constant acceleration, motion under constantly increasing (decreasing) acceleration, or something else. Since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer. The answer depends on whether it is uniform motion, motion under constant acceleration, motion under constantly increasing (decreasing) acceleration, or something else. Since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.
When should army safety inspections be performed?
It depends on what needs inspection. All items have certain safety functions to be performed at certain intervals.
If the derivative of a function equals xsquared - 2divided byx on which intervals is f decreasing?
f(x) is decreasing on the interval on which f'(x) is negative. So we want: (x2-2)/x<0 For this to be true either the numerator or the denominator (but not both) must be negative. On the interval x>0, the numerator is negative for 0<x<sqrt(2) and the denominator is positive for all x>0. On the interval x<0, the denominator is negative for all values on this interval. The numerator is positive on this interval for x<-sqrt(2). So, f' is negative (and f is decreasing) on the intervals: (-infinity, -sqrt(2)), (0, sqrt(2))
Who created the periodic law?
that many of the physical and chemical properties of the elements tend to recur in a systematic manner with increasing atomic number.
What has the author Robert G Potter written?
Robert G. Potter has written: 'Comparison of three acceptance strategies' -- subject(s): Birth control, Birth intervals, Case studies, Contraception, Mathematical models
Would the data be better displayed on a histogram minute intervals or minute intervals?
Perhaps minute intervals might be better than minute intervals.
