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f(x) = 2x^3 - 9ax^2 + 12a^2 x + 1 has local max at p and local min at q with p^2 = q

The same question, asked 2 times: 8 Apr 2024*, 2 Apr 2025. Every wording below, oldest first.

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  1. Question 1

    8 Apr 2024

    164
    If the function f(x)=2x3−9ax2+12a2x+1,a>0f(x) = 2x^{3}- 9ax^{2}+ 12a^{2}x+ 1,a> 0 has a local maximum at x=αx =\alpha and a local minimum x=α2x=\alpha^{2}, then α\alpha and α2\alpha^{2} are the roots of the equation :

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  2. Question 2

    2 Apr 2025

    59
    If the function f(x)=2x3−9ax2+12a2x+1f(x) = 2x^{3}- 9ax^{2}+ 12a^{2}x+ 1, where a >0> 0, attains its local maximum and local minimum values at pp and qq, respectively, such that p2=qp^{2}= q, then f(3)f(3) is equal to:

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