If the function $f(x)=2{x}^{3}-9a{x}^{2}+12{a}^{2}x+1,a0$ has a local maximum at $x=\alpha$ and a local minimum at $x={\alpha }^{2}$, then $\alpha$ and ${\alpha }^{2}$ are the roots of the equation : [JEE Main 2024, 8 Apr (Shift 2)]

Question

If the function $f(x)=2{x}^{3}-9a{x}^{2}+12{a}^{2}x+1,a>0$ has a local maximum at $x=\alpha$ and a local minimum at $x={\alpha }^{2}$, then $\alpha$ and ${\alpha }^{2}$ are the roots of the equation : [JEE Main 2024, 8 Apr (Shift 2)]

YESPYQ · Accepted Answer

Options are free to see. Unlock the correct answer and full explanation with PYQ Pass.

If the function \(f(x)=2{x}^{3}-9a{x}^{2}+12{a}^{2}x+1,a>0\) has a local maximum at \(x=\alpha\) and a local minimum at …

Practice more JEE Maths PYQs