The function f(x)=x^3-3 x^2+3 x-100, x R is ....... - Vidyadip

MCQ

The function $f(x)=x^3-3 x^2+3 x-100, x \in R$ is $.......$

✓
increasing.
B
decreasing
C
increasing and decreasing
D
neither increasing nor decreasing

✓

Answer

Correct option: A.

increasing.

$f(x)=x^3-3 x^2+3 x-100, x \in R$
$f^{\prime}(x)=3 x^2-6 x+3$
$=3\left(x^2-2 x+1\right)$
$=3(x-1)^2$
Since$, (x – 1)^2$ is always positive $x \neq 1$
$f'(x) > 0$ for all $x \in R, x \neq 1$
Hence$, f (x)$ is an increasing function, for all $x \in R, x \neq 1$

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