Question: Let f be a function given by f ( x ) = 4 x 3 . What is the instantaneous rate of change of f

Let f be a function given by f(x)=4x3. What is the instantaneous rate of change of f at a, where a is any real number?
The rate of change is given by f(a), and so is the slope of the tangent line to the curve y=f(x) at the point (a,f(a)).
The derivative is the slope of the line y=4x3! Therefore, f(a)=, for all real numbers a.

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