If a function is not continuous at a number, then it is not differentiable becau

Question

If a function is not continuous at a number, then it is not differentiable because

continuity at a point implies differentiability at a point.

Trick question. A function can be differentiable at a point where it is not continuous.

Because the jump discontinuity creates a vertical tangent line.

if a function is discontinous at a point, then the limit that defines the derivative does not exist.

continuity at a point implies differentiability at a point.

Trick question. A function can be differentiable at a point where it is not continuous.

Because the jump discontinuity creates a vertical tangent line.

if a function is discontinous at a point, then the limit that defines the derivative does not exist.

Explanation / Answer

The theorem that is best to look at here, states that,

"If a function is differentiable at a, then it is continuous at a."

The converse, even, is not true. The converse, which is,

"If a function is continuous at a, then it is differentiable at a,"
so option d..if a function is discontinous at a point, then the limit that defines the derivative does not exist.

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