Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

If $f (x) = sin^{2} x cos^{2} x ℓ cos^{2} x ℓ sin^{2} x ℓ sin^{2} x cos^{2} x$ , where $ℓ$ is a root of $16 ℓ^{2} - 16 ℓ + 7 = 0$ , then there exist two real numbers $(a, b) \in (0, \frac{π}{2})$ and $a < b$ for which $f (x) = 0$ . Does there exist $c \in (a, b)$ for which $f^{'} (c) = 0$ ? Then

The value of 'b' is

Options:

Answer:

Solution:

From f(x) = (ℓ+1)(ℓ² − ℓ + 1 − (3/4)sin²2x) with ℓ² − ℓ + 1 = 9/16 (as 16ℓ² − 16ℓ + 7 = 0), f(x) = 0 ⇒ sin²2x = 3/4 ⇒ sin2x = √3/2 on (0, π/2), so the two roots are x = π/6 and x = π/3. The larger root is b = π/3.

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

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...