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The derivative can be thought of as the slope of the line tangent to a curve at any given point. If you graph the expression y = 3, for example, it is just a horizontal line intercepting the y axis at 3. The slope of that line is, of course, equal to zero, for any point on the curve (which in this case is a straight line). Therefore, the derivative (with respect to x) of y = 3 is zero. Since the slope of any horizontal line is zero, the derivative of any line of the form y = k, where k is a constant, is zero.
Answer2:
Any constant quantity and an expression that has a maximum or minimum or both, has a derivative equal to zero.
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What is the derivative of square root of 3?
The derivative of ANY constant expression - one that doesn't depend on variables - is zero.
Where the graph of a function equals the value zero?
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
What is a nonzero number?
A quantity which does not equal zero is said to be nonzero.
For what value of x is the rational expression below equal to zero?
2
What does it mean for a function when the graph of the derivative crosses the x-axis?
This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.
