Question

The function $f\left(x\right)=2x^3-3\left(a+b\right)x^2+6abx$ has a local maximum at $x=a,$ if

• A. $a>b$
• B. $a<b$
• C. $a>0$
• D. $a<0$

Answer 1

Answer: (B)

$f^{{}^{\prime }}\left(x\right)=6\left(x^2-\left(a+b\right)x+ab\right)$
$=6\left(x-a\right)\left(x-b\right)$

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