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Derivative of zero

Updated: 4/28/2022
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13y ago

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The derivate of zero - as well as the derivative of ANY constant (non-variable) number, is zero. (A graph of y = 0 for example will be a horizontal line - the slope is zero.)

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What is the derivative of 0?

If you mean "what is the deriviative of f(x) = 0?", the answer is 0. (zero) The deriviative of any constant is zero.


Is it always true that between any two zeros of any polynomial there is a zero of the derivative?

Yes.


What is the rate of change of a horizontal line?

The rate of change of any function is its derivative. The equation of a horizontal line is simply a constant, for example y=10. The derivative of any constant is ZERO.


How do you determine the relative minimum and relative maximum values of functions and the intervals on which functions are decreasing or increasing?

You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.


How do you know if a point is a maximum or a minimum?

Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.