What does it mean If f''>0 for all x in an interval

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What does it mean If f''>0 for all x in an interval

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Well, f'' is the second derivative. The second derivative is the derivative of the first derivative. The first derivative describes how fast the base function (f) is changing at a given point. The second derivative describes how fast the derivative is changing. If f'' > 0 for all x in an interval, that means the first derivative is increasing for that interval, which means that the rate of change of f is constantly increasing in that interval. Does that help?
Simplifying the previous answer somewhat, f'' describes concavity. When f'' is positive, the curve is concave up (like a smile). When f'' is negative, the curve is concave down (like a frown).
thanks a lot

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