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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.
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 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.
What function always has a derivative of 0?
f(x) = c, where c is constant, has a derivative of zero.
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.
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.
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 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.
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.
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.
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 non-exponential function is its own derivative?
The only non-exponential function that has this property would be a function that has the constant value of zero.
What is the rate of change of a horizontal line?
The rate of change of any function is its derivative. The equation of a horizontal line is simply a constant, for example y=10. The derivative of any constant is 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.
Why does you put c after integration?
When you find an indefinite integral of a function (ie, the integral of a function without integration limits) you are actually finding the antiderivative of that function. In other words, you are finding the function whose derivative is the function 'inside' the integral sign. Recall that the derivative of a constant is zero. The point here is that you add the 'c' to acknowledge the fact that when the derivative of the result of your integration effort is taken to get the original function it could, or would, have been followed by some unknown constant value that disappeared upon differentiation. That constant is denoted by the 'c'.
