# Consider the following statements: 1. The derivative where the function attains maxima or minima must be zero. 2. If a function is differentiable at a

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Consider the following statements:

1. The derivative where the function attains maxima or minima must be zero.

2. If a function is differentiable at a point, then it must be continuous at that point.

Which of the above statements is/are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
5. None of these

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Correct Answer - Option 3 : Both 1 and 2

Concept:

Statement 1 is true, The derivative where the function attains maxima or minima must be zero.

At the point of the local maxima or minima, the derivative of the function must be 0, such that the tangent at that point is parallel to the x-axis.

Statement 2 is also true, If a function is differentiable at a point, then it must be continuous at that point and so the vice versa is also true.