Notes I took while in Calculus class.

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Average Rate of Change in output with respect to input= f(a+h)-f(a)/h or (change in output over change in inputs).

Instantaneous Rate of Change of f with respect to x = lim h--> 0 f(a+h)-f(a)/h

Derivative of function f at x=a : f’(a) = lim h--> 0 f(a+h)-f(a)/h

The tangent line to the graph of f at x=a is the line passing through the point (a,f(a)) with slope f’(a).