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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

If $f (x)$ is a differentiable function wherever it is continuous, and $f^{'} (c_{1}) = f^{'} (c_{2}) = 0$ , $f^{''} (c_{1}) < f^{''} (c_{2}) < 0$ , $f (c_{1}) = 5$ , $f (c_{2}) = 0$ , and $c_{1} < c_{2}$ .

If $f (x)$ is continuous in $[c_{1}, c_{2}]$ and $f^{''} (c_{1}) - f^{''} (c_{2}) < 0$ then the minimum number of roots of $f^{'} (x) = 0$ in $[c_{1} - 1, c_{2} + 1]$ is

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Answer:

Solution:

$f^{''} (c_{1}) < 0 f^{''} (c_{2}) > 0$ It follows that $f^{'} (x) = 0$ has at least two roots in the given interval

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Rolle's-theroem

⏱ 2mℹ️ Source: QB

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