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The existence of a derivative function at a given point depends on the behavior of the original function at that point. A derivative exists at a point if the function is continuous and has a defined slope (i.e., is differentiable) at that point. However, there are functions that are not differentiable at certain points—such as those with sharp corners, vertical tangents, or discontinuities—meaning the derivative does not exist for all values of ( x ). Thus, while many functions are differentiable everywhere, not all functions possess derivatives across their entire domain.
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All the values that go into a function. All of the input or independent values what is this called?
They are called the arguments of the function.
What set of all values that a function can take as is called domain of the function?
Actually, the set of all values that a function can take is referred to as the "range" of the function, not the domain. The domain of a function is the set of all possible input values (or independent variables) for which the function is defined. In contrast, the range consists of all output values that result from applying the function to its domain.
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
How can you find the domain and range of a function?
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
The set of all output values of a function?
That set is called the ranger of the 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
Is signum function differentiable?
The signum function, also known as the sign function, is not differentiable at zero. This is because the derivative of the signum function is not defined at zero due to a sharp corner or discontinuity at that point. In mathematical terms, the signum function has a derivative of zero for all values except at zero, where it is undefined. Therefore, the signum function is not differentiable at zero.
All the values that go into a function. All of the input or independent values what is this called?
They are called the arguments of the function.
The set of all values that a function will return as outputs is called the of the function?
The set of all values that a function will return as outputs is called the *range* of the function.
What set of all values that a function can take as is called domain of the function?
Actually, the set of all values that a function can take is referred to as the "range" of the function, not the domain. The domain of a function is the set of all possible input values (or independent variables) for which the function is defined. In contrast, the range consists of all output values that result from applying the function to its domain.
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.
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
How can you find the domain and range of a function?
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
f(x)= – x2f′′(x)=?
The function given is (f(x) = -x^2). The second derivative of a function, denoted as (f’'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (f’(x)) is (-2x). Taking the derivative of (f’(x)) gives us the second derivative (f’‘(x)), which is (-2). So, (f’'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.
What is the set of all possible output values of a function or relation?
The Range is the set of all possible output values of a function or relation.
What are all the x values in a function?
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Which best describe the domain of a function?
The set of values for which the function is defined.
