Find Increasing Intervals for y = 2x² - 4x + 5: Quadratic Function Analysis

To determine where the function $y = 2x^2 - 4x + 5$ is increasing, we must first find its derivative and analyze its behavior.

Step 1: Find the derivative of $y$.
The function given is $y = 2x^2 - 4x + 5$. The first derivative, which represents the slope of the tangent at any point $x$, is found by differentiating:
$y' = \frac{d}{dx}(2x^2 - 4x + 5) = 4x - 4$

Step 2: Set the derivative to greater than zero and solve for $x$.
We set the inequality to determine where the function is increasing:
$4x - 4 > 0$

• Add 4 to both sides to isolate the linear term:
  $4x > 4$
• Divide both sides by 4 to solve for $x$:
  $x > 1$

Thus, the function is increasing for all $x > 1$.

Therefore, the correct answer is $x > 1$.