Question

The function $f\left(x\right)=x^2+2x-5$ is strictly increasing in the interval

• A. $(-\infty ,-1)$
• B. $(-\infty ,-1]$
• C. $[-1,\infty )$
• D. $(-1,\infty )$

Answer 1

Answer: (D)

$(-1,\infty )$

$f\left(x\right)=x^2{}^{}+2x-5$
$f^{{}^{\prime }}\left(x\right)=2x+2$
When $x<-1,f^{{}^{\prime }}\left(x\right)<0$
When $x>-1,f^{{}^{\prime }}\left(x\right)>0$
$\therefore$ For $x>-1,f\left(x\right)$ is strictly increasing
$\therefore (-1,\infty )$