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Q: What is the average rate of change for this quadratic function for the interval from x 3 to x 5?

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The mean value theorem for differentiation guarantees the existing of a number c in an interval (a,b) where a function f is continuous such that the derivative at c (the instantiuous rate of change at c) equals the average rate of change over that interval. mean value theorem of integration guarantees the existing of a number c in an interval (a,b)where a function f is continuous such that the (value of the function at c) multiplied by the length of the interval (b-a) equals the value of a the definite integral from a to b. In other words, it guarantees the existing of a rectangle (whose base is the length of the interval b-a that has exactly the same area of the region under the graph of the function f (betweeen a and b).

It equals an undefined entity. The average acceleration of an object equals the CHANGE in velocity divided by the time interval. The term "change in velocity" is not the same as the term "velocity", "average velocity", or "instantaneous velocity".

In general, the acceleration during that time interval could vary considerably. However, we can calculate the average acceleration during the interval. The change in speed is 20 meters per second - 5 meters per second = 15 meters per second, and this change in speed occurs over a 3 second interval. Thus the average change in speed over this interval is 15 meters per second/ 3 seconds = 5 meters per second per second = 5 meters/second2

Average acceleration during the time interval = (change on speed) / (time for the change) =(98 - 121) / (12) = -23/12 = negative (1 and 11/12) meters per second2

V = d / tVelocity is the change in distance over an interval of time.

Related questions

what exponential function is the average rate of change for the interval from x = 7 to x = 8.

To find the average rate of change over an interval, you can calculate the difference in the function values at the endpoints of the interval, and then divide by the difference in the input values. This gives you the slope of the secant line connecting the two points, which represents the average rate of change over that interval.

The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.

The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).

Average acceleration is the change in velocity divided by the change in time over a certain interval. Instantaneous acceleration is the acceleration of an object at a specific moment in time, which can be found by taking the derivative of the velocity function with respect to time.

The average acceleration during the time interval from 0 to 10 seconds is the change in velocity divided by the time interval. If you provide the initial and final velocities during this time interval, we can calculate the average acceleration for you.

The mean value theorem for differentiation guarantees the existing of a number c in an interval (a,b) where a function f is continuous such that the derivative at c (the instantiuous rate of change at c) equals the average rate of change over that interval. mean value theorem of integration guarantees the existing of a number c in an interval (a,b)where a function f is continuous such that the (value of the function at c) multiplied by the length of the interval (b-a) equals the value of a the definite integral from a to b. In other words, it guarantees the existing of a rectangle (whose base is the length of the interval b-a that has exactly the same area of the region under the graph of the function f (betweeen a and b).

It equals an undefined entity. The average acceleration of an object equals the CHANGE in velocity divided by the time interval. The term "change in velocity" is not the same as the term "velocity", "average velocity", or "instantaneous velocity".

Average velocity can be calculated by dividing the displacement (change in position) by the time interval. The formula for average velocity is average velocity = (final position - initial position) / time interval.

Average velocity is change in position (displacement) divided by the interval.

There have to be two (or more) ordered pairs for an average rate of change to make any sense. Your question does not.

If the function is continuous in the interval [a,b] where f(a)*f(b) < 0 (f(x) changes sign ) , then there must be a point c in the interval a<c<b such that f(c) = 0 . In other words , continuous function f in the interval [a,b] receives all all values between f(a) and f(b)