Understanding the Positive Derivative: How it Indicates an Increasing Function

When f ‘(x) is positive, f(x) is

When f ‘(x) is positive, it means that the derivative of the function f(x) with respect to x is greater than 0

When f ‘(x) is positive, it means that the derivative of the function f(x) with respect to x is greater than 0. In other words, the slope of the graph of f(x) is positive at that point.

This tells us that as x increases, the value of f(x) also increases. In other words, the function f(x) is increasing in the interval where f ‘(x) is positive.

Graphically, this can be represented by an upward sloping line or curve. As x moves to the right, the corresponding values of f(x) move up.

For example, let’s consider the function f(x) = 2x^2. The derivative of f(x) is f ‘(x) = 4x. When x is positive (greater than 0), the derivative f ‘(x) is positive, indicating that the function is increasing.

If we plot the graph of f(x) = 2x^2, we can see that it is an upward parabola. As x increases, the corresponding values of f(x) also increase. This confirms that when f ‘(x) is positive, f(x) is increasing.

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