Question

The function $f\left(x\right)=\pi x^{3}-\frac{3 \pi }{2}\left(a + b\right)x^{2}+3\pi abx$ has a local minimum at $x=a,$ then the values $a$ and $b$ can take are

• A. $a=\pi ,b=e$
• B. $a=e,b=\pi $
• C. $a=b=\pi $
• D. $a=b=e$

Answer 1

Answer: (B)

$f^{'} \left(x\right) = 3 \pi \left(x^{2} - \left(a + b\right) x + a b\right)$
$=3\pi \left(x - a\right)\left(x - b\right)$

i.e. $f\left(x\right)$ has a local maximum at $x=a,$ if $a < b$