Use the rules in Exercise 48 and the Linearity Rules to prove the first part of Theorem

Question:

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

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

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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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Nov 11, 2023 08:22 AM

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Use the rules in Exercise 48 and the Linearity Rules to prove the first part of Theorem

Question:

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.

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Let fx mx b Then fx mx ...View the full answer

Calculus

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