Yes, it is possible for the instantaneous rate of change to be 0. For a specific example, imagine the function #f(x) = 3#. This is a horizontal line parallel to the x-axis at the value y=3. This function is unchanging for any value of x, therefore its rate of change is zero.

This simple equation is called the slope formula. If #y = f(x+h) = 3 (x + h)^ 2#, (Just plug x + h in for x). So, you get this: The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point. #y' = f'(x+h) = (d/(dx)) (3*(x)^2) = 6x * 1 = 6x#

2014年7月31日 · Instantaneous rate of change of a function is represented by the slope of the line, it tells you by how much the function is increasing or decreasing as the #x#-values change. Figure 1. Slope of a line. In this image, you can see how the blue function can have its instantaneous rate of change represented by a red line tangent to the curve.

2017年9月15日 · The instantaneous rate of reaction is the slope of the line (the tangent to the curve) at any time t. (From SPM Chemistry) How do we determine it? We draw the best tangent to the line that we can and extend it to convenient points on the axis that will make it easy to calculate the value of (Δ["P"])/(Δt) For example, the graph below shows the ...

2015年3月28日 · The instantaneous rate of change is the derivative which is defined as lim_(Delta x ->0)(f(x+Deltax)-f(x))/(Delta x)

2017年12月2日 · You approximate it by using the slope of the secant line through the two closest values to your target value. Sometimes there are more requirements, but in AP Calculus you almost always end up taking the values to the left and right of your target value and calculating based on them. x | f(x) 1 | 3 2 | 5 3 | 4 4 | 9 From the "table" we'd approximate the following: …

2018年4月15日 · As below. Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: . This simple equation is called the slope formula. If y = f(x+h) = 3 (x + h)^ 2, (Just plug x + h in for x). So, …

Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of h, to find the instantaneous rate of change for the given function at the given value. f(x)=5x ln x; x=3 The instantaneous rate of change for the function at x=3 is _____. (Do not round until the final answer.

2014年8月12日 · As an exercise, suppose that I tell you that the instantaneous rate of change of the function #f(x) = x^3 -1# at the point #x=2# is 12. You can estimate this by using intervals of different size. In this case, try first the interval #[-1,5]# followed by the interval #[0,4]# and then the interval #[1,3]#. You should notice that as your interval ...