Question

The function $y=x^{4}-8x^{3}+22x^{2}-24x+10$ attains local maximum or minimum at $x=a, \, x=b$ and $x=c \, \left(a < b < c\right).$ Then $a, \, b$ and $c$ are in

• A. Geometric progression
• B. Harmonic progression
• C. Arithmetic progression
• D. None of these

Answer 1

Answer: (C)

$\frac{d y}{d x}=4x^{3}-24x^{2}+44x-24$
$=4\left(x^{3} - 6 x^{2} + 11 x - 6\right)$
$=4\left(x - 1\right)\left(x - 2\right)\left(x - 3\right)$
So, $\frac{d y}{d x}=0$ at $x=1, \, 2, \, 3$
which are the points of local extremum.
i.e., $a=1$
$b=2$
$c=3$
Hence, $a, \, b, \, c$ are in $AP$