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2. Theory of the Derivative 2.1 Tangent Lines 2.2 Definition of - PowerPoint PPT Presentation

May 31, 2023 •25 likes •1.08k views

2. Theory of the Derivative 2.1 Tangent Lines 2.2 Definition of Derivative 2.3 Rates of Change 2.4 Derivative Rules 2.5 Higher Order Derivatives 2.6 Implicit Differentiation 2.7 LHpitals Rule 2.8 Some Classic Theoretical Results

  1. sin( x ) Compute lim x → 0 x

  2. cos( x ) Compute lim x → 0 x

  3. 2.8 Some Classic Theoretical Results

  4. • This is not a course in theory, but certain results are important for the CLEP. • Proving these would be an excellent learning experience, but is certainly not necessary. A basic understanding would suffice for the CLEP exam.

  5. Differentiability Implies Continuity Suppose a function f is di ff erentiable at a point x. Then f is continuous at x.

  6. Rolle’s Theorem Suppose a function f is di ff erentiable on an interval ( a, b ) . If f ( a ) = f ( b ) , then there is a point c, a < c < b such that f 0 ( c ) = 0 .

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