Calculate Positive Area: Finding Area of f(x)=2x²-50

To solve this problem, we'll follow these steps:

• Step 1: Solve the equation $2x^2 - 50 = 0$ to find the roots.
• Step 2: Analyze intervals on the number line based on the roots to find where $f(x) > 0$.

Now, let's work through each step:
Step 1: Set the function to zero: $2x^2 - 50 = 0$. Solving gives:

Step 2: The roots divide the number line into intervals: $x < -5$, $-5 < x < 5$, and $x > 5$. We test these intervals in $f(x) = 2x^2 - 50$.

• For $x < -5$, pick $x = -6$: $f(-6) = 2(-6)^2 - 50 = 72 - 50 = 22 > 0$ This interval is positive.
• For $-5 < x < 5$, pick $x = 0$: $f(0) = 2(0)^2 - 50 = -50 < 0$ This interval is negative.
• For $x > 5$, pick $x = 6$: $f(6) = 2(6)^2 - 50 = 72 - 50 = 22 > 0$ This interval is positive.

Therefore, the function is positive for $x < -5$ and $x > 5$.

Hence, the solution to the problem is $x < -5$ or $5 < x$.