Suppose mathrmx1 mathrmx2 are the point of maximum and the point of minimum respectively of the function f(x)=2 x3-9 a x2+12 a2 x+1 respectively, then for the equality x12=x2 to be true the value of 'a' must be

Question

Suppose mathrmx1 mathrmx2 are the point of maximum and the point of minimum respectively of the function f(x)=2 x3-9 a x2+12 a2 x+1 respectively, then for the equality x12=x2 to be true the value of 'a' must be (A) 0 (B) 2 (C) 1 (D) 1 / 4

Tardigrade Admin · Accepted Answer

f prime(x)=6(x2-3 a x+2 a2)=6(x-2 a)(x-a)=0 ⇒ x=2 a text or a f prime prime(x)=6(2 x-3 a)

Q. Suppose $x_{1} & x_{2}$ are the point of maximum and the point of minimum respectively of the function $f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1$ respectively, then for the equality $x_{1}^{2} = x_{2}$ to be true the value of 'a' must be

0

2

1

$1/4$

$f^{'} (x) = 6 (x^{2} - 3 a x + 2 a^{2}) = 6 (x - 2 a) (x - a) = 0 \Rightarrow x = 2 a or a$
$f^{''} (x) = 6 (2 x - 3 a)$

Q. Suppose x1​&x2​ are the point of maximum and the point of minimum respectively of the function f(x)=2x3−9ax2+12a2x+1 respectively, then for the equality x12​=x2​ to be true the value of 'a' must be

0

2

1

1/4

f′(x)=6(x2−3ax+2a2)=6(x−2a)(x−a)=0⇒x=2a or a f′′(x)=6(2x−3a)

Q. Suppose $x_{1} & x_{2}$ are the point of maximum and the point of minimum respectively of the function $f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1$ respectively, then for the equality $x_{1}^{2} = x_{2}$ to be true the value of 'a' must be

$1/4$

$f^{'} (x) = 6 (x^{2} - 3 a x + 2 a^{2}) = 6 (x - 2 a) (x - a) = 0 \Rightarrow x = 2 a or a$
$f^{''} (x) = 6 (2 x - 3 a)$