Find Increasing Intervals: Analyzing y = (x+10)(x-8)

To determine the intervals where the function $y = (x+10)(x-8)$ is increasing, we will follow these steps:

• Step 1: Expand the expression for clarity.
• Step 2: Find the derivative $y'$ of the expanded function.
• Step 3: Determine where $y' > 0$ to identify increasing intervals.

Step 1: Expand the function $y = (x+10)(x-8)$.

Expanding gives: $y = x^2 + 2x - 80$.

Step 2: Find the derivative $y'$ of $y = x^2 + 2x - 80$.

$y' = \frac{d}{dx}(x^2 + 2x - 80) = 2x + 2$.

Step 3: Find where the function is increasing by solving $y' > 0$.

$2x + 2 > 0$.

Solve for $x$:

$2x > -2$

$x > -1$.

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

Therefore, the solution to the problem is $x > -1$.