Question
If the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$, where $a>0$, attains its maximum and minimum at $p$ and $q$ respectively such that $p^{2}=q$, then $a$ equals $\quad$ [2003](A) 3(B) I(C) 2(D) $\frac{1}{2}$
Step 1
We need to find the maximum and minimum of this function. To do this, we first find the derivative of the function with respect to $x$. $$f'(x) = 6x^{2}-18ax+12a^{2}$$ Show more…
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If the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$, where $a>0$, attains its maximum and minimum at $x=p$ and $x=q$ respectively such that $\mathrm{p}^{2}=\mathrm{q}$, then the value of ${ }^{\prime} \mathrm{a}$ is (a) 2 (b) $\frac{1}{4}$ (c) $\frac{1}{8}$ (d) 4
If the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$, where $a>0$, attains its max. and min. at $p$ and $q$ respectively such that $p^{2}=q$ then $a$ is (a) $\frac{1}{2}$ (b) 1 (c) 2 (d) 3
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