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3 cases in which Derivatives don’t exist.

3 cases in which Derivatives don’t exist. Case 1: F(x) is discontinuous at x = a. If a function has any type of disconuity at x = a, then does not exist. Examples: does not have a derivative at x = 0 The graphs below have no derivatives at x = 1,1 & 0 respectively.

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3 cases in which Derivatives don’t exist.

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  1. 3 cases in which Derivatives don’t exist.

  2. Case 1: F(x) is discontinuous at x = a • If a function has any type of disconuity at x = a, then does not exist. • Examples: • does not have a derivative at x = 0 • The graphs below have no derivatives at x = 1,1 & 0 respectively .

  3. Case 2: Sharp turn, bend or cusp • If the function’s graph has a sharp turn, bend or cusp, the derivative at that point does not exist. • No derivative at x = -1 or 2 No derivative at x = 0 or 6

  4. Case 3: Vertical tangents • If the tangent to the graph of is completely vertical, the derivative at that point does not exist. • Examples: • has no derivative at x = 0 • No derivative at x = 1.5 No derivative at x = 0

  5. In general… • Functions only have derivatives where it is smooth and continuous.

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