This is a direct consequence of the Mean Value Theorem. If the derivative of a function is zero throughout an interval, it means the rate of change of the function is zero everywhere in that interval. Consequently, the value of the function does not change, making it a constant function over the specified interval.
If a function has differential coefficient that vanishes for all values of x in the interval A<=x <=b, the function is?
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Question context
This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the SPSC – Sindh Public Service Commission preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.