Increasing Functions In Calculus: Positive Derivatives And Upward Slopes

When f ‘(x) is positive, f(x) is

increasing

When f ‘(x) is positive, it means that the function f(x) is increasing at that point x. In other words, as x increases, the value of f(x) also increases. This can be seen visually on a graph as an upward slope.

For example, let’s say we have a function f(x) = x^2. When we take the derivative of f(x), we get f ‘(x) = 2x.

If we pick a point on the graph, say x = 2, and evaluate f ‘(x) at that point, we get f ‘(2) = 2(2) = 4.

Since f ‘(2) is positive, we know that at x = 2, the function f(x) is increasing. In other words, as we move to the right of x = 2, the values of f(x) will continuously increase.

So, we can conclude that when f ‘(x) is positive, f(x) is increasing at that point x.

More Answers:
Mastering Calculus: Identifying Local Maximum At X Using Derivatives
Local Minimum: How The Function’S Slope Determines Its Lowest Point
The Significance Of F'(X) Being Negative In Math: Implications For Function Decrease

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