At any x, if first order and second order derivatives of a function f is equal to 0 and greater than 0 respectively, then1 pointx is a local maximum of fx is a local minimum ofx is a stationary pointNone of the above
Question
At any x, if first order and second order derivatives of a function f is equal to 0 and greater than 0 respectively, then1 pointx is a local maximum of fx is a local minimum ofx is a stationary pointNone of the above
Solution
The answer is "x is a local minimum of f".
Here's why:
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The first derivative of a function at a point gives the slope of the tangent at that point. If the first derivative is zero, it means the tangent is horizontal at that point. This could indicate a local maximum, a local minimum, or a point of inflection.
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The second derivative of a function at a point gives the curvature of the function at that point. If the second derivative is greater than zero, it means the function is concave up at that point. This indicates a local minimum.
Therefore, if the first derivative is zero and the second derivative is greater than zero at a point x, then x is a local minimum of the function f.
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