Find the instantaneous rate of change of the function f(x)=3x^2 as x approaches 3.

The instantaneous rate of change as x approaches 3 is 18.

Step-by-step explanation:

From Differential Calculus and Geometry we remember that instantaneous rate of change of the function is represented by a tangent line, whose slope is determined by the first derivative of the curve. Let , the instantaneous rate of change of the function when x approaches 3 is deducted from the definition of derivative:

(1)

(2)

If we know that , then the instantaneous rate of change as x approaches 3 is:

The instantaneous rate of change as x approaches 3 is 18.