Question

Find the points of local maxima/minima of following functions
$f\left(x\right)=2x^3-21x^2+36x-20$

• A. local max. at $x=-1$, local min. at $x=-6$
• B. local max. at $x=6$, local min. at $x=1$
• C. local max. at $x=1$, local min. at $x=6$
• D. None of these

Answer 1

Answer: (C)

local max. at $x=1$, local min. at $x=6$

$f^{\prime }\left(x\right)=6x^2-42x+36=0$
Or
$6(x^2-7x+6)=0$
Or
$(x-6)(x-1)=0$
$x=6$ and $x=1$.
$f"\left(x\right)=12x-42$
Now
$f"\left(1\right)=-30$
Hence point of maxima.
$f"\left(6\right)=30$
Hence point of minima.