section36_material

section36_material - MATH110BUSINESSCALCULUS

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MATH 110 BUSINESS CALCULUS CHAPTER 3 INTRODUCTION TO THE DERIVATIVE Section 3.6 The Derivative: Algebraic Viewpoint We’ll start with an example: Example: Compute f’(a) algebraically for the given value of a. 2 () 4 ; 6 fx x a =− = Solution: By definition, 0 22 0 2 0 2 00 0 (6 ) (6) (6) lim (6 ) 4 (6 4) lim 36 12 4 36 4 lim 12 (12 ) lim lim lim(12 ) 12. h h h hh h fh f f h h h h h h h →→ +− = −− = ++ + = == = + =
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MORE Examples: 1. Compute f’(a) algebraically for the given value of a. ( ) 3 7 ; 2 fx x a =− + 2. Compute f’(a) algebraically for the given value of a. 2 () 9 ; 8 x x a =+ = 3. Compute f’(a) algebraically for the given value of a. 3 ( ) 9 3 ; 4 x x a = 4. Compute f’(a) algebraically for the given value of a. 9 () ; 5 a x =
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5. Compute f’(x) 2 () 4 f xx x =− Solution to # 5:
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section36_material - MATH110BUSINESSCALCULUS

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