Calculate Ascending Area: Finding Area Under f(x)=2x²

Video Solution

Solution Steps

00:00 Find the domain of increase of the function

00:04 We'll examine the coefficient of X squared, it's positive so the function is happy

00:08 We'll examine the trinomial coefficients

00:16 We'll use the formula to find the vertex of the parabola

00:21 We'll substitute appropriate values according to the given data and solve to find the vertex

00:27 This is the X value at the vertex of the parabola

00:32 We'll determine based on the type of parabola when it's decreasing and when it's increasing

00:37 We'll draw the X-axis and find the domain of increase

00:41 And this is the solution to the question

Step-by-Step Solution

To determine the intervals where the function $f(x) = 2x^2$ is increasing, we will analyze the derivative of the function:

Step 1: Differentiate the function.
The derivative of $f(x) = 2x^2$ is $f'(x) = 4x$ .

Step 2: Determine where $f'(x) > 0$ .
To find the increasing intervals, set $4x > 0$ . Solving this inequality, we obtain $x > 0$ .

Therefore, the function $f(x) = 2x^2$ is increasing for $x > 0$ .

Consequently, the correct answer is the interval where the function is increasing, which is $0 < x$ .