Let f ( x ) = ( sin θ ) ( x 2 − 2 ) (( sin θ ) x + cos θ ) , ( θ  = m π , m ∈ I ) Then f ( x ) has

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumsingle choice

Let $f (x) = (sin θ) (x^{2} - 2) ((sin θ) x + cos θ), (θ \neq = m π, m \in I)$ Then $f (x)$ has

Answer:

Solution:

$f (x) = (sin^{2} θ) x^{3} + \frac{1}{2} sin 2 θ x^{2} - 2 sin^{2} θ . x - sin 2 θ$ $f^{'} (x) = (3 sin^{2} θ) x^{2} + sin 2 θ x - 2 sin^{2} θ$

Then D > 0 and product of roots < 0

So $f (x)$ has local maxima at some $x \in R^{-}$ and local minima at some $x \in R^{+}$

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

⏱ 2mℹ️ Source: QB

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