The instantaneous rate of change is the change in the rate at a specific instant, and it is equal to the derivative value at that specific point. For the function f x = 2 x 2 + 2, the instantaneous rate of change at x = 5 is calculated as:
(a) Find the average rate of change of g from x = -5 to x = 5. (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not exist. (c) On what open intervals, if any, is the graph of g concave up? Justify your answer. (d) Find all x- values in the interval -5 < x < 5 at which g has a critical point.
The goal is to find a point where the tangent to the curve (instantaneous rate of change) matches the secant between \ ( a ) and \ ( b ) (average rate of change).
For how many values of x in the open 2 interval (0, 1.565) is the instantaneous rate of change of f equal to the average rate of change of f on the closed interval [0, 1.565] ?
The figure above shows the graph of the differentiable function f for 1 ≤ x ≤ 11 and the secant line through the points (1, f (1)) and (11, f (11)). For how many values of x in the closed interval [1, 11] does the instantaneous rate of change of fat x equal the average rate of change of f over that interval?
The graph of the function P and the line tangent to Pat t = 8 are shown above. Which of the following gives the best estimate for the instantaneous rate of change of Pat t = 8?