Question

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

Answer 1

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