The function f(x) = x² + 2x - 5 is strictly increasing in the interval:

Concept:

For a function y = f(x):

• At the points of local maxima or minima, f'(x) = 0.
• In the regions where f(x) is increasing, f'(x) > 0.
• In the regions where f(x) is decreasing, f'(x) < 0.

Calculation:

For the function f(x) = x2 + 2x - 5 to be strictly increasing, f'(x) > 0.

⇒ f'(x) = 2x + 2 > 0

⇒ x > -1

⇒ x ∈ (-1, ∞).