CUET · MATHS · PYQ PAPER 2023
If \(y=f(x)\) is continuous on the interval \([a, b]\) max \(y\) occurs at a point \(c\), and \(f^{\prime}(c) \neq 0, f^{\prime}(c)\) exists than :
- A \(c\) is equal to a but not \(b\)
- B \(c\) is equal to \(b\) but not a
- C \(c\) is equal to \(a\) or \(b\)
- D \(c\) is equal to mid value of \(a\) and \(b\)
Answer & Solution
Correct Answer
(C) \(c\) is equal to \(a\) or \(b\)
Step-by-step Solution
Detailed explanation
\(c\) must be an endpoint since \(f^{\prime}(c) \neq 0\) for a maximum. \(c = a\) or \(c = b\)
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