KCET2008MathematicsContinuity and Differentiability

f(x)= cases 2 a-x & in -a < x < a 3 x-2 a & in a x cases Then, which of the following is true ?

Options

Af(x) is discontinuous at x=a
Bf(x) is not differentiable at x=a
Cf(x) is differentiable at x a
Df(x) is continuous at all x < a

Correct answer

B. f(x) is not differentiable at x=a

Step-by-step solution

Given, f ( x )= array llc 2 a - x & in & -a It is clear from the graph that f ( x ) is continuous everywhere it is also differentiable everywhere except a point A at x = a .

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