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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))
Difference between power series and fourier power series?
A power series is a series of the form ( \sum_{n=0}^{\infty} a_n (x - c)^n ), representing a function as a sum of powers of ( (x - c) ) around a point ( c ). In contrast, a Fourier power series represents a periodic function as a sum of sine and cosine functions, typically in the form ( \sum_{n=-\infty}^{\infty} c_n e^{i n \omega_0 t} ), where ( c_n ) are Fourier coefficients and ( \omega_0 ) is the fundamental frequency. While power series are generally used for functions defined on intervals, Fourier series specifically handle periodic functions over a defined period.
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 is the difference between augmented and diminished intervals in music theory?
Augmented intervals are larger than perfect or major intervals, while diminished intervals are smaller. Both alter the size of a perfect or major interval by either increasing (augmented) or decreasing (diminished) it by a half step.
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.
What information can be found in the augmented and diminished intervals chart?
The augmented and diminished intervals chart provides information about the distance between notes in a musical scale that have been altered by either increasing (augmented) or decreasing (diminished) their natural distance.
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 distinguishes consonant intervals from dissonant intervals in terms of their harmonic properties?
Consonant intervals are harmonically stable and pleasing to the ear due to their simple mathematical ratios, while dissonant intervals create tension and are less stable because their ratios are more complex.
How do you recognize a periodic trend on the periodic table?
A periodic trend is recognized by observing how a property changes as you move across or down the periodic table. If the property shows a repeating pattern or periodicity, such as consistently increasing or decreasing values at regular intervals, then it is likely a periodic trend. Common examples include atomic radius increasing down a group or ionization energy increasing across a period.
What is the definition of non uniform speed?
Non-uniform speed refers to an object moving at a speed that is changing, either increasing or decreasing. This means that the object is not maintaining a constant velocity over time.
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.
