Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemHard2 minQB

MathematicsHardsingle choice

Continuous twice-differentiable $f, g$ satisfy $f (0) = f (3) = 0, f (1) f (2) < 0$ , and $g (0) = g (3) = 0$ . The number of roots of $f'' (x) g (x) + f' (x) g' (x) = 0$ in (-1, 5) cannot be

Options:

Answer:

Solution:

$f$ has at least three zeros, so $f /$ has at least two. Together with the two zeros of $g$ , the product $f / g$ has at least four zeros. Rolle then gives at least three zeros of $(f / g) / = f // g + f / g /$ . Therefore two roots are impossible.

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

⏱ 2mℹ️ Source: QB

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