Tamil Nadu Board of Secondary EducationHSC Science Class 11

The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable. - Mathematics

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Graph

The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.

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Solution

We know A function f is not differentiable at a point x0 belonging to the domain of f if one of the following situations holds

(i) f has a vertical tangent at x0

(ii) The graph of f comes to a point at x0 ......(either a sharp edge ∨ or a sharp peak ∧)

For the given graph f

At x = – 1, a sharp edge ∨

At x = 8, a sharp peak ∧

At x = 4, discontinuity

At x = 11, perpendicular tangent

∴ The given graph is not differentiable at

x = – 1, 8, 4, 11

Concept: Differentiability and Continuity
  Is there an error in this question or solution?
Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.1 [Page 147]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.1 | Q 5 | Page 147

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