Question

$f\left(x\right)=x^3-6x^2+12x-16$ is strictly decreasing for

• A. $x\in R$
• B. $x\in R-\left\{1\right\}$
• C. $x\in R^{+}$
• D. $x\in \varphi$

Answer 1

The correct option is D $x\in \varphi$

A function is strictly decreasing in the range when $\frac{d\left(f\right(x\left)\right)}{dx}<0$

$\frac{d\left(f\right(x\left)\right)}{dx}=3x^2-12x+12=3(x^2-4x+4)=3(x-2{)}^2$

Since the square of any number is non negative, we don't find any value of $x$ for which the function would be strictly decreasing.