Question

Which of the following option(s) is/are correct regarding the intervals of concavity of the function $f\left(x\right)$ denoted by $f\left(x\right)=3x-x^3$ :

• A.
  Concave up for $x\in (-\infty ,0)$
  
• B. Concave down for $x\in (-\infty ,0)$
• C. Concave down for $x\in (0,\infty )$
• D. Concave up for $x\in (0,\infty )$
  

Answer 1

Answer: (A), (C)

Concave down for $x\in (0,\infty )$

$f\left(x\right)=3x-x^3$
$f^{\prime }\left(x\right)=3-3x^2$
$f^{\prime \prime }\left(x\right)=-6x$
Concave up for $x\in (-\infty ,0)$
Concave down for $x\in (0,\infty )$