QJEEM21Ma1cc4: JEE Main 2021 Mathematics - Class 12 JEEM21Ma1cc4 Solution: Let 'a' be a real number such that the function f(x) = ax 2 +…

Question

Verified Solution • 2025–26 Session moderate

Let 'a' be a real number such that the function f(x) = ax² + 6x

-

15, x

\in

R is increasing in

(- \infty, \frac{3}{4})

and decreasing in

(\frac{3}{4}, \infty)

. Then the function g(x) = ax²

-

6x + 15, x

\in

R has a :

Accepted Answer

\frac{- B}{2 A} = \frac{3}{4}

\Rightarrow \frac{- (6)}{2 a} = \frac{3}{4}

\Rightarrow a = \frac{- 6 \times 4}{6} \Rightarrow a = - 4

∴

g (x) = 4 x^{2} - 6 x + 15

Local max. at

x = \frac{- B}{2 A} = - \frac{(- 6)}{2 (- 4)}

= \frac{- 3}{4}

Step-by-Step Verified Solution