Calculate Ascending Area: Finding Area of y=(x+3)²+2x²

To solve this problem, we will use the following steps:

• Step 1: Differentiate the function.
• Step 2: Find where the derivative is greater than zero.
• Step 3: Use the inequality to determine the increasing interval.

Let's proceed with the solution:

Step 1: Differentiate the given function with respect to $x$:

$y = (x+3)^2 + 2x^2$

Differentiate each term:

$\frac{d}{dx}((x+3)^2) = 2(x+3) \cdot 1 = 2(x+3)$

$\frac{d}{dx}(2x^2) = 4x$

Combine the derivatives:

$y' = 2(x+3) + 4x = 2x + 6 + 4x$

$y' = 6x + 6$

Step 2: Find the values of $x$ where the derivative is greater than zero:

$6x + 6 > 0$

Simplify the inequality:

$6x > -6$

$x > -1$

Step 3: The solution to the inequality tells us the interval where the function is increasing:

The function is increasing wherever $x > -1$.

Therefore, the correct answer is $-1 < x$.