Question

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

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

Answer 1

Answer: (A)

$(-1, \infty)$

Answer 2

We have $f(x) =x^{2}+2 x-5$ $\Rightarrow \, f'(x) =2 x+2$ $=2(x+1)$ $\therefore \, f'(x) \geq \,0$ $\Rightarrow 2(x+1) \geq\, 0$ $\Rightarrow x+1 \geq\, 0$ $\Rightarrow x \geq-1$ $\therefore$ f(x) is increasing on $[-1, \infty)$