Instantaneous Rate of Change
The Formula of Instantaneous Rate of Change represented with limit exists in,
With respect to x, when x=a and y = f(x)
Solved Example
Problem 1: Compute the Instantaneous rate of change of the function f(x) = 3x2 + 12 at x = 4 ?
Answer:
Known Function,
y = f(x) = 3x2 + 12
f'(x) = 3(2x) + 0
f'(x) =6x
Thus, the instantaneous rate of change at x = 4
f'(4) = 6(4)
f'(4) = 24
Problem 2: Compute the Instantaneous rate of change of the function f(x) = 5x3 – 4x2 + 2x + 1 at x = 2?
Answer:
Known Function,
y = f(x) = 5x3 – 4x2 + 2x + 1
f'(x) = 5(3x2) – 4(2x) + 2 + 0
f'(x) = 15x2 – 8x + 2
Thus, the instantaneous rate of change at x = 2
f'(2) = 15(2)2 – 8(2) + 2 = 60 – 16 + 2 = 46
f'(2) = 46
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