The function f is continuous on the interval (0,9) and is twice differentiable except at x = 6, where the derivatives do not exist (DNE). Information about the first and second derivatives of f for some values of x in the interval (0,9) is given in the table above. Which of the following statements could be false?

A continuous function f(x) does not have discontinuity at any point

The statement that could be false is (c). The function f has a relative minimum at x = 6.

The interval is given as:

Interval = (0,9)

From the question, we understand that the function is not differentiable at x = 6.

This means that the function may or may not have a relative minimum at x = 6.

Hence, the statement that could be false is (c).

Read more about continuous functions at:

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The statement that could be false is;

(C) The function has a relative minimum at x = 6

Step-by-step explanation:

The given parameters are;

The function is continuous in the interval 0 ≤ x ≤ 9

The function is not differentiable at x = 6

f prime (x) = Negative for 4 < x < 6, and positive for 6 < x < 8

Therefore, at x = 6, the function is vertical

The statement that could be false is that the function has a relative minimum at x = 6.