Question

For the function $f\left(x\right)=\sin x+x^2+3x,$ which of the following is true regarding its monotonicity at $x=0$

• A. Increasing
• B. Decreasing
• C. Non-monotonic
• D. Can't be determined

Answer 1

The correct option is A Increasing

$f\left(x\right)=\sin x+x^2+3x$
$f^{\prime }\left(x\right)=\cos x+2x+3$
$f^{\prime }\left(0\right)=1+0+3=4>0$
$\Rightarrow f\left(x\right)$ increasing at $x=0$