Question

The graph of $y=x^3+x-2$ is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Given : $y=x^3+x-2,$ Domain $\in R$ and Range $\in R$
Now, $y=0$ gives $x=1$ and
at $x=0,y=-2$
$y^{\prime }=3x^2+1>0,x\in R\left(\text{monotonically increasing}\right)$
$y^{\prime \prime }=6x$
$\Rightarrow y^{\prime \prime }=0$ at $x=0$ (point of inflection)
$y^{\prime \prime }>0$ for $x>0$ (concave up)
$y^{\prime \prime }<0$ for $x<0$ (concave down)
Now, plotting the graph :