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