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.
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