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What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
How many x-intercepts can a function defined on an interval have if it is increasing on that interval?
One.
What tables represent an exponential function. Find the average rate of change for the interval from x 7 to x 8.?
what exponential function is the average rate of change for the interval from x = 7 to x = 8.
Can you Give an example of bounded function which is not Riemann integrable?
Yes. A well-known example is the function defined as: f(x) = * 1, if x is rational * 0, if x is irrational Since this function has infinitely many discontinuities in any interval (it is discontinuous in any point), it doesn't fulfill the conditions for a Riemann-integrable function. Please note that this function IS Lebesgue-integrable. Its Lebesgue-integral over the interval [0, 1], or in fact over any finite interval, is zero.
What is the area bounded by the graph of the function fx equals 1 - e to the power of -x over the interval -1 2?
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
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 characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
What function f whose arc length from to x is 2x?
It is mathematically impossible to use arc length and an interval alone to determine a function!
How does knowing the zeros of a function help determine where a function is positive?
Knowing the zeros of a function helps determine where the function is positive by identifying the points where the function intersects the x-axis. Between these zeros, the function will either be entirely positive or entirely negative. By evaluating the function's value at points between the zeros, one can determine the sign of the function in those intervals, allowing us to establish where the function is positive. This interval analysis is crucial for understanding the function's behavior across its domain.
When is a function would be positive real function?
A function is positive on an interval, say, the interval from x=a to x=b, if algebraically, all the y-coordinate values are positive on this interval; and graphically, the entire curve or line lies above the x-axis.on this interval.
How many x-intercepts can a function defined on an interval have if it is increasing on that interval?
One.
Determine which is the graph of the function Here is the equation httptinyurlcom4bzq4m Here is choice's 1-2-3-4 httptinyurlcom49u2og httptinyurlcom3ernxz httptinyurlcom5xkelp httptinyurlcom4g8r4q?
The question was, let f(x) = 2x if x < -2, ...2x - 2 if -2 <= x <= 2, and ...-2 if x < -2; and what is its graph. You might call this a piecewise-defined linear function. The easiest way to determine this is to look at each interval and see: * Is the function a straight line on each whole interval? * Can you pick two points on each interval so that they match the equation? * And is it a function? Do that and you'll be able to tell. E-mail me if you have more questions on this.
Is it true that a continuous function that is never zero on an interval never changes sign on that interval?
Yes.
Can interval notation be used when defining the range of a function?
Yes.
What happens to the confidence interval as the standard deviation of a distribution increases?
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
What is range of 1 divide by 1 plus square rootx?
2
How can one determine the position of an object from a velocity graph?
To determine the position of an object from a velocity graph, you can find the area under the velocity curve. The area represents the displacement of the object. The position can be calculated by integrating the velocity function over a specific time interval.
