Calculate the Area of f(x) = x²: Positive Region Analysis

Question

Find the positive area of the function

f(x)=x2 f(x)=x^2

Video Solution

Solution Steps

00:00 Find the positive domain of the function
00:03 Note the coefficient of X squared is positive, therefore the function is smiling (opens upward)
00:11 The positive domain is above the X-axis
00:14 Therefore, we substitute Y=0 to find the intersection points with the X-axis
00:20 This is the intersection point of the function with the X-axis
00:24 Let's mark the intersection points with the X-axis
00:36 The positive domain is above the X-axis
00:40 And this is the solution to the question

Step-by-Step Solution

To determine where the function f(x)=x2 f(x) = x^2 is positive, we consider the nature of this parabolic graph, which opens upwards.

Step 1: Recognize that the function f(x)=x2 f(x) = x^2 outputs non-negative values for any real number x x . The graph of this function is a U-shaped parabola.

Step 2: Analyze the values of the function:
- For x=0 x = 0 , f(0)=02=0 f(0) = 0^2 = 0 .
- For x0 x \neq 0 , f(x)=x2>0 f(x) = x^2 > 0 , because squaring any non-zero real number results in a positive value.

Therefore, the function is positive for all x x except at x=0 x = 0 , where it is zero.

Step 3: Based on the comparison given in the choices, and our calculation, the area of interest is positive for x0 x \neq 0 .

Thus, the solution to the problem is that the positive area occurs for x0 x \neq 0 .

Answer

x0 x≠0