Yes, it has to be zero because the derivative must change sign. Same for minima.
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That refers to the highest and lowest value of a function. A "local maximum" (or local minimum) refers to a value that is higher than any near-by value, for a certain neighborhood.
An "extreme value" is either a local maximum, or a local minimum - i.e., a point which is greater than all the points in a certain neighborhood, or less than all points in a certain neighborhood.
(1) Derivatives are useful tools for providing information about the behaviour of the graph.(2)Derivatives helps to measure the steepness of the graph.(3)Derivatives gives us information wether the graph is increasing or decreasing.(4) Derivatives Helps us to determine maximum,minimum value,and crital pointsof graph. hope it will help Kalim Raja
A global minimum is a point where the function has its lowest value - nowhere else does the function have a lower value. A local minimum is a point where the function has its lowest value for a certain surrounding - no nearby points have a lower value.
It has a face value of 5 but a local value of 5000