The average rate of change of the function over the interval [0,2] is 1.5 The average rate of change of the function over the interval [0,2] is 0.5 Here the end points are (0,0.5) and (2,2.5) We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a. What is Rate of Change (ROC) The rate of change - ROC - is the speed at which a variable changes over a specific period of time. ROC is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, Look at the slope in the example below and compare it to Example 2 above. Which slope is steepest? Which shows the greatest rate of change? Both graphs show a decline of $50 per month. They both show the same rate of change. It is only the difference in scale of the y-axis that makes Example 2 appear steeper. 1 Expert Answer. Rate of change can be either positive (acceleration) or negative (deceleration). Therefore, it is the magnitude (absolute value) that determines the "amount" of rate of change. Bottom line: -4 is a greater rate of change than +2 (assuming the units are the same in both instances). Differentiating the function will give its slope. Since slope is defined as the rate of change, then getting the maxima of the function's derivative will indicate where it is increasing at the greatest rate. Applying the first derivative test, the critical number is $\sqrt{\frac{11}{3}}$. Algebra 2: Functions of All types help? 1) f(x) = 3 cos 2x + 4. h(x) x y-6 -11-5 -6-4 -3-3 -2-2 -3-1 -6. 0 -11. Which of those functions has the greatest maximum y-value? -3 -27-2 -8-1 -1. 0 0. 1 1. 2 8. 3 27. 4 64. h(x) = (x + 4)2 + 2. Which one of these two functions has the greatest rate of change on the interval from x=o to x=4? 3) f(x
A summary of Rates of Change and Applications to Motion in 's Calculus AB: Thus, the derivative shows that the racecar had an instantaneous velocity of 24 In a world of constant change, the spoils go to the nimble. Perhaps most important, they have learned to unlock their greatest resources—the For example, a leading media company that was suffering from a high rate of customer successful online platform, which has extended the company's business model, enabling Generally speaking, the rate of change as x approaches infinity increases as the degree of the function increases. Because g(x) = 5x^2 - x + 7 has the highest degree (2 as opposed to 1) it has the greatest rate of change for when x approaches infinity. #1 x and y have equal rates of change #2 y has the greater rate of change. #3 clearly y changes faster. Heck, they told you that in just so many words.
In a world of constant change, the spoils go to the nimble. Perhaps most important, they have learned to unlock their greatest resources—the For example, a leading media company that was suffering from a high rate of customer successful online platform, which has extended the company's business model, enabling Generally speaking, the rate of change as x approaches infinity increases as the degree of the function increases. Because g(x) = 5x^2 - x + 7 has the highest degree (2 as opposed to 1) it has the greatest rate of change for when x approaches infinity.
This means that the rate of change is $100 per month. Therefore, John saves on average, $100 per month for the year. This gives us an "overview" of John's savings per month. Best Answer. c has the greatest rate of change, which can be determined by the slope in y=mx+b. a. slope=2 y=2x-2. b. slope=4/3 y=(4/3)x+1. c. slope=2.5
"over which interval does y(x) have an average rate of change of 5/2?" a graph is provided with five seemingly random horizontal segments, spread across the 3 Mar 2019 Rate of change is identical to slope, so using points (1,0) and (3,5), you can tell the slope is 5/2, or 2.5. 2.5 is smaller than 3, so it must be A. Sorry