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Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
What is an increment on a graph?
a thing on math
Derivative of zero?
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.)
How can sketch a graph of a derivative?
To sketch a graph of a derivative, first look at the points where your original function f(x) has any horizontal tangents. If is does at that horizontal tangent plot a point correspondingly on the x-axis. From here analyze your functions in intervals. Where the f(x) function is increasing, your derivative function f prime of x should always be above the x axis, and conversely, where f(x) is decreasing your derivative function should always be below the axis As a crucial step, you should look at locations within the original function that are endpoints, cusps. and undefined points. This is essential as the derivative of the function will be undefined at those locations, and must be shown clearly on the graph (which is usually resolved with an open circle). To best understand sketching derivatives, try experimenting with a derivative plotter (java applet that can usually be found on-line for free. Also try to imagine the tangents to the original graph, as the graph progresses. Lastly, it should be noted that the magnitude of your derivative will depend on the rate of change of the function. However, most calculus teachers will let this be arbitrary.
What is the difference between nonlinear and linear functions?
Linear function:No variable appears in the function to any power other than 1.A periodic input produces no new frequencies in the output.The function's first derivative is a number; second derivative is zero.The graph of the function is a straight line.Non-linear function:A variable appears in the function to a power other than 1.A periodic function at the input produces new frequencies in the output.The function's first derivative is a function; second derivative is not zero.The graph of the function is not a straight line.
What is a derivative graph?
A derivative graph tracks the slope of a function.
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.
Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
What is the highest point on a graph?
The highest point on a graph is when the derivative of the graph equals 0 or the slope is constant.
Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
Does a derivative exist if the graph goes through the origin?
It may or may not exist. Whether or not the graph goes through the origin does not in any way affect whether or not it has a derivative. A function has a derivative if it has no discontinuities, cusps, sharp corners, or vertical tangents.
What is an increment on a graph?
a thing on math
How do you graph the slope of a function?
For example, if the slope at a certain point is 1.5, you can draw a line that goes through the specified point, with that slope. The line would represent the slope at that point. If you want to graph the slope at ALL POINTS, take the derivative of the function, and graph the derivative. The derivative shows the slope of a function at all points.
How do you graph trigonometric functions?
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
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 are uses of derivatives?
A derivative of a function represents that equation's slope at any given point on its graph.
What shows acceleration an a speed time graph?
The slope is the acceleration. Acceleration is the time derivative of velocity.
