Question

If differentiation of any function is zero at any point and constant at other points then it means?

Answer 1

Answer:

Suppose a function f(x) is continuous on [a,b] and differentiable on (a,b). If f is constant, then of course it has always-zero derivative. Conversely, if f'(x)=0 on (a,b) (in other words, if the derivative vanishes everywhere on (a,b)), then f must be constant

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Answer 2

Answer:

Suppose a function f(x) is continuous on [a,b] and differentiable on (a,b). If f is constant, then of course it has always-zero derivative. Conversely, if f'(x)=0 on (a,b) (in other words, if the derivative vanishes everywhere on (a,b)), then f must be constant.