Use the rules in Exercise 48 and the Linearity Rules to prove the first part of Theorem 1 in Section 3.1.

Data From Exercise 48

Prove each of the following using the definition of the derivative.
The First-Power Rule: d/dx x = 1
The Constant Rule: d/x c = 0

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THEOREM 1 Derivative of Linear and Constant Functions If f(x) = mx + b is a linear function, then f'(a) = m for all a. • If f(x) = b is a constant function, then f'(a) = 0 for all a.