Question

The function $f\left(x\right)=2x^3-9x^2+12x+29$ is monotonically decreasing function, when

• A. $x<2$
• B. $x>2$
• C. $x>1$
• D. $1<x<2$

Answer 1

The correct option is A $x<2$

Differentiate the given function $f\left(x\right)=2x^3-9x^2+12x+29$.

$f^{\prime }\left(x\right)=6x^2-18x+12$

Put $f^{\prime }\left(x\right)=0$, then,

$6x^2-18x+12=0$

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

$x^2-2x-x+2=0$

$x\left(x-2\right)-1\left(x-2\right)=0$

$\left(x-1\right)\left(x-2\right)=0$

$x=1,2$

At $x=1$, the value of given function becomes,

$f\left(1\right)=2{\left(1\right)}^3-9{\left(1\right)}^2+12\left(1\right)+29$

$=34$

At $x=2$, the value of given function becomes,

$f\left(2\right)=2{\left(2\right)}^3-9{\left(2\right)}^2+12\left(2\right)+29$

$=33$

Therefore, this shows that the given function decreases at $x<2$.