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The derivative if a function is basically it's slope, or its rate of change.
An example is the function y = 4x - 6. This is a line with a slope of 4. The derivative is y' = 4.
Another example is the function y = 3x2. This is a parabola with a vertex at (0,0). Its derivative is y' = 6x. At x = 0, the slope of the parabola is 6*0, which is 0, since this is the vertex of the parabola. To the left, at x is -4 for example, the derivative (and therefore slope) is negative. To the right, at x = 5 for example, the derivative is positive. The farther away from the vertex, the greater the value of the derivative so the the slope of the function increases as you move away from the vertex (it gets steeper).
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How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
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.
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.
What is the derivative of e2x-1?
3
How can you determine if a relationship between two variables is a function from a graph?
The relationship is a function if a vertical line intersects the graph at most once.
Relationship between Integration and differentiation?
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
What is the second derivative of a function's indefinite integral?
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
What is the difference between differentiation and a differential equation?
Differentiation: when you differentiate a function, you find a new function (the derivative) which expresses the old function's rate of change. For example, if f(x) = 2x, then the derivative f ' (x) = 2 for all x, because the function is always increasing by 2 units for every increase of x by 1 unit.A differential equation is an equation expressing a relationship between a named function and its derivatives. This can be as simple as y = y', where y is the original function and y' the derivative.
Relationship between integral and derivative?
The Derivative is the instantaneous rate of change of a function. An integral is the area under some curve between the intervals of a to b. An integral is like the reverse of the derivative, Derivatives bring functions down a power, integrals bring them up, in-fact indefinite integrals (ones that do not have specifications of the area between a to b) are called anti derivatives.
What is the purpose of differential calculus?
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
What is the difference between differential and derivative in the field of calculus?
The derivative refers to the rate at which a function changes with respect to another measure. The differential refers to the actual change in a function across a parameter. The differential of a function is equal to its derivative multiplied by the differential of the independent variable . The derivative of a function is the the LIMIT of the ratio of the increment of a function to the increment of the independent variable as the latter tends to zero.
What is null derivative?
A null derivative occurs when an increasing function does not have a derivative. This is most commonly seen in the question mark function.
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
What is the relationship between chest circumference and lung function test?
what is the relationship between chest circumference and lung function test
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 the geometrical meaning for second derivative?
The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.
What is the function if the first derivative of a function is a constant?
A linear function, for example y(x) = ax + b has the first derivative a.
