The function y=x4-8x3+22x2-24x+10 attains local maximum or minimum at x=a, x=b and x=c (a

Question

The function y=x4-8x3+22x2-24x+10 attains local maximum or minimum at x=a, x=b and x=c (a < b < c). Then a, b and c are in (A) Geometric progression (B) Harmonic progression (C) Arithmetic progression (D) None of these

Tardigrade Admin · Accepted Answer

(d y/d x)=4x3-24x2+44x-24 =4(x3 - 6 x2 + 11 x - 6) =4(x - 1)(x - 2)(x - 3) So, (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

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

Geometric progression

Harmonic progression

Arithmetic progression

None of these

$\frac{d y}{d x} = 4 x^{3} - 24 x^{2} + 44 x - 24$
$= 4 (x^{3} - 6 x^{2} + 11 x - 6)$
$= 4 (x - 1) (x - 2) (x - 3)$
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 $A P$

Q. The function y=x4−8x3+22x2−24x+10 attains local maximum or minimum at x=a,x=b and x=c(a<b<c). Then a,b and c are in