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What is the function if the first derivative of a function is a constant?
Wiki User
∙ 14y ago
A linear function, for example y(x) = ax + b has the first derivative a.
Wiki User
∙ 14y ago
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What is the significance of the first derivative of a function to be a constant?
If the first derivative if a function is a constant that the original function has only one slope across its entire domain, so it is a line.
What is the derivative of the the constant function?
zero
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.
What function always has a derivative of 0?
f(x) = c, where c is constant, has a derivative of zero.
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 significance of the first derivative of a function to be a constant?
If the first derivative if a function is a constant that the original function has only one slope across its entire domain, so it is a line.
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 derivative of the the constant function?
zero
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.
What is the derivative of just a constant?
0 A derivative is the rate of change of a function as another variable changes. As there is no change to a constant, the derivative is necessarily 0.
What is the derivative of 2001?
derivative of a constant is 0, because the function of a constant is a line with no change in slope, so d2011/dx=0
What function always has a derivative of 0?
f(x) = c, where c is constant, has a derivative of zero.
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.
If second derivative is 0 and third derivative is 0 What is true about that point?
If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.
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 does the constant rate mean in math?
It means that the first derivative is a constant. The derivative may be with regard to time or any other variable.
What is the double prime of 5x?
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
