f(x) is increasing -> f'(x) is
positive
positive
If the function f(x) is increasing, it means that as x increases, the value of f(x) also increases. This implies that the slope of the function at any given point is positive because the function is moving upwards.
The derivative of a function f'(x) represents the slope of the function at any given point. So, if f(x) is increasing, the derivative f'(x) is positive. This is because a positive derivative means that the slope of the function is positive at any given point, which in turn means that the function is increasing in value.
In other words, when f'(x) is positive, the function is increasing.
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