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Application of Derivatives question

2024 · 8 Apr · Shift 2 · Q47

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PYQ Library
JEE Main
Mathematics
Application of Derivatives
2024 · 8 Apr · Shift 2 · Q47

Application of Derivatives question

2024 · 8 Apr · Shift 2 · Q47

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

If the function

f(x)=2 x^3-9 \mathrm{ax}^2+12 \mathrm{a}^2 x+1, \mathrm{a}\gt 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 :

A
$x^2-6 x+8=0$
B
$8 x^2-6 x+1=0$
C
$8 x^2+6 x-1=0$
D
$x^2+6 x+8=0$

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