Instantaneous Rate of Change Formula

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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