Question

The value of the parameter a for which the value the function $f\left(x\right)=x^3-{6x}^2+9x+a$ at the point $x=2$ and at the points of extrema, taken in a certain order, form a geometric progression are

• A. $0$
• B. $-\frac{8}{3}+\frac{4}{3}$
• C. $\frac{8}{3}-\frac{4}{3}$
• D. $-\frac{8}{3}-\frac{4}{3}$

Answer 1

The correct option is A $0$

$f\left(x\right)=x^3-6x^2+9x+a$

$x=2$

$8-6\left(4\right)+18+4=0$

$a=-2$

$3x^2-12x+9=0$

$3(x^2-4x+3)=0$

$3(x-1)(x-3)=0$