NDA2018MathematicsContinuity and DifferentiabilityActual

For the function f(x)=|x-3| , which of the following is not correct?

Options

AThe function is not continuous at x=-3
BThe function is continuous at x=3
CThe function is differentiable at x=0
DThe function is differentiable at x=-3

Correct answer

A. The function is not continuous at x=-3

Step-by-step solution

gathered f(x)=|x-3| f(x)= cases (x-3), & x 3 (3-x), & x 3 cases f^ (x) at x=3⁺=1 f^ (x) at x=3⁻=-1 gathered Thus, f(x) is not differentiable at x=3 but f(x) is continuous at x=3 .

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