KCET2013MathematicsContinuity and Differentiability

If f(x)= array l 2 a-x when -a < x < a 3 x-2 a when a x array . . Then, which of the following is true?

Options

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

Correct answer

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

Step-by-step solution

Given, f(x)= array l 2 a-x, when -a < x < a 3 x-2 a, when a x array . Now, f^ (x)= array cl -1, & when -a < x < a 3, & when a x array . L f^ (a)=-1 and R f^ (a)=3 i.e., L f^ (a) R f^ (a) Hence, f(x) is not differentiable at x=a .

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