Find the interval in which function f(x) = x2 – 4x + 5 is increasing

The correct option is (2, ∞).

To find the interval in which the quadratic function
$$f(x)=x^2-4x+5$$
is increasing, we need to determine where its first derivative is strictly positive, i.e., $f^{\prime }(x)>0$.

Step 1: Find the derivative of the function
We apply the power rule of differentiation to each term of the function:
$$f^{\prime }(x)=\frac{d}{dx}(x^2-4x+5)$$
$$f^{\prime }(x)=2x-4$$

Step 2: Set up the inequality for an increasing function
A function is increasing on an interval where its derivative is positive:
$$f^{\prime }(x)>0$$
Substituting the derivative we found:
$$2x-4>0$$

Step 3: Solve the inequality for x
Add 4 to both sides of the inequality:
$$2x>4$$
Divide both sides by 2:
$$x>2$$

Conclusion:
Since $x>2$, the function is increasing on the interval from 2 to infinity, which is represented in interval notation as (2, ∞).