Calculate Area Under (x+5)²: Finding the Descending Region

Find the descending area of the function

$y=(x+5)^2$

To solve this problem, we will determine when the function $y = (x+5)^2$ is decreasing by using its derivative:

• Step 1: Differentiate $y = (x+5)^2$ with respect to $x$, yielding $\frac{dy}{dx} = 2(x+5)$.
• Step 2: Set the derivative less than zero: $2(x+5) < 0$.
• Step 3: Simplify the inequality to solve for $x$:
  $x + 5 < 0$ implies $x < -5$.

The function is decreasing for values of $x$ that satisfy $x < -5$.

Therefore, the solution is $x < -5$.