Find the intervals in which f(x) = x2 + 2x – 5 is strictly increasing

The correct option is x > -1.

To find the intervals in which the function $f\left(x\right)=x^2+2x-5$ is strictly increasing, we need to analyze its first derivative.

Recall that a function $f\left(x\right)$ is strictly increasing on an interval if its derivative with respect to $x$ is strictly greater than zero for all points in that interval. That is:
$f^{\prime }\left(x\right)>0$

First, let's find the derivative of the given function:
$f\left(x\right)=x^2+2x-5$

Differentiating both sides with respect to $x$ using the power rule:
$f^{\prime }\left(x\right)=\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(2x\right)-\frac{d}{dx}\left(5\right)$
$f^{\prime }\left(x\right)=2x+2$

Now, set the derivative strictly greater than zero to determine the interval where the function is strictly increasing:
$2x+2>0$

Solving this inequality for $x$:
Subtract 2 from both sides:
$2x>-2$
Divide both sides by 2:
$x>-1$

Thus, the function is strictly increasing in the interval defined by x > -1 (or in interval notation, $(-1,\infty )$).