Question

If $f\left(x\right)=x^3-10x^2+200x-10$, then f (x) is

• A. decreasing $(-\infty ,10]$ and increasing in $(10,\infty )$
• B. increasing $(-\infty ,10]$ and decreasing in $(10,\infty )$
• C. increasing for every value of x
• D. decreasing for every value of x

Answer 1

The correct option is C increasing for every value of x

$f\left(n\right)=x^3-10x^2+200x-10$

$f^1\left(n\right)=3n^2-20x+200$

$3n^2-20x+200=0$

$1<0$

always increasing $f\times h$