Let f ( x ) = ab sin x + b 1 − a 2 cos x + c , where ∣ a ∣ 0 , then

f ( x ) = a 2 b 2 + b 2 − b 2 a 2 sin ( x + α ) + c = b sin ( x + α ) + c where tan α = a 1 − a 2 . ( f ( x ) ) max − ( f ( x ) ) min = 2 b . Also, at x = − cos − 1 a , f ( x ) = c .

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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediummultiple choice

Let $f (x) = ab sin x + b 1 - a^{2} cos x + c$ , where $∣ a ∣ < 1, b > 0$ , then

Options:(select one or more)

Answer:

A, B, C

Solution:

$f (x) = a^{2} b^{2} + b^{2} - b^{2} a^{2} sin (x + α) + c = b sin (x + α) + c$ where $tan α = \frac{1 - a ^{2}}{a} . (f (x))_{max} - (f (x))_{min} = 2 b$ . Also, at $x = - cos^{- 1} a, f (x) = c$ .

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

⏱ 2mℹ️ Source: QB

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