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Understanding Differentiability: Identifying Functions and Derivatives

Explore how functions may fail to be differentiable with vertical tangents at x=a, Chapter 3 delves into various differentiation problems and techniques including finding slopes and limits, trigonometric function derivatives, and utilizing the chain rule. Linearization and differentials are also discussed.

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Understanding Differentiability: Identifying Functions and Derivatives

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  1. Exam2: Differentiation HOW CAN A FUNCTION FAIL TO BE DIFFERENTIABLE? Definition: the curve has a vertical tangentlinewhen x = a 1) f is cont at a 2)

  2. Chapter3: Differentiation

  3. Chapter3: Differentiation

  4. Chapter3: Differentiation TERM-121 Exam-2

  5. Chapter3: Differentiation

  6. Chapter3: Differentiation

  7. Chapter3: Differentiation Exam-2 Problems • Direct: Find the g’(2) • Indirect: Find the slope…. • Find slope in different ways • Find • Find: lim • Find f’(x) • others

  8. Sec 3.5:Derivatives Of Trigonometric Functions

  9. Sec 3.5:Derivatives Of Trigonometric Functions

  10. Sec 3.5:Derivatives Of Trigonometric Functions

  11. Chapter3: Differentiation

  12. Chapter3: Differentiation Exam-2 Problems • Direct: Find the g’(2) • Indirect: Find the slope…. • Find slope in different ways • Find • Find: lim • Find f’(x) • others

  13. Chapter3: Differentiation

  14. Chapter3: Differentiation Chain Rule: Chain Rule:

  15. Chapter3: Differentiation

  16. Chapter3: Differentiation

  17. Sec 3.11:Linearization and Differentials

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