f’=0
f is constant
The equation f’=0 means that the derivative of the function f is equal to zero. When the derivative of a function is zero, it means that the function is constant. This is because the derivative of a constant function is always zero.
To find the function f that satisfies this equation, we can integrate both sides with respect to some independent variable x. Integrating the left-hand side yields f(x) + C, where C is the constant of integration. Integrating the right-hand side just gives the constant of integration, which we can also write as C.
Therefore, the general solution to the equation f’=0 is f(x) = C, where C is any constant. This means that the function f is a constant function, with its output value always equal to C for every input value of x.
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