Question

Which of the following option correctly defines the intervals of concavity of $f\left(x\right)=x+\sqrt{x}$ :

• A. Concave down in $:x\in (0,\infty )$
• B. Concave up only in $:x\in (2,\infty )$
• C. Concave up only in $:x\in (0,\infty )$
• D. Concave down only in $:x\in (2,10)$

Answer 1

The correct option is A Concave down in $:x\in (0,\infty )$

$f\left(x\right)=x+\sqrt{x}$
$f^{\prime }\left(x\right)=1+\frac{1}{2\sqrt{x}}$
$f"\left(x\right)=\frac{-1}{4x\sqrt{x}}$
Concave down in : $x\in (0,\infty )$