If the function f(x)=2 x^3-9 a x^2+12 a^2 x+1, where a>0, attains… - Vidyadip

MCQ

If the function $f(x)=2 x^3-9 a x^2+12 a^2 x+1$, where $a>0$, attains its local maximum and local minimum values at p and q , respectively, such that $p ^2= q$, then $f(3)$ is equal to:

A
55
B
10
C
23
✓
37

✓

Answer

Correct option: D.

37

(D) 37
Explanation: $f^{\prime}(x)=6 x^2-18 a x+12 a^2$
$f(x)=6\left(x^2-3 a x+2 a^2\right)$
roots are $a , 2 a$
$p^2=q \Rightarrow a^2=2 a$
$\begin{array}{l}a=2 \\
f(x)=2 x^3-18 x^2+48 x+1\end{array}$
$f(3)=37$

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