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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumsingle choice

If $f (x) = 2 x^{3} - 3 (p + 2) x^{2} + 12 p x + ln (16 - p^{2})$ has exactly one local maximum and one local minimum, then $p$ belongs to

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Answer:

Solution:

The logarithm requires $- 4 < p < 4$ . Also $f_{'} = 6 [x^{2} - (p + 2) x + 2 p]$ has two distinct roots when its discriminant $(p - 2)^{2}$ is positive, so $p \neq = 2$ . Intersecting gives $(- 4, 4) \ {2}$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

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