the graph of f'(x) is above the x-axis at x=2
f(x) is increasing when x=2
When the graph of f'(x) is above the x-axis at x=2, we can say that the function f(x) is increasing at x=2.
To understand why this is true, we need to know the definition of the derivative: the derivative of f(x) at x=a represents the instantaneous rate of change of f(x) at x=a.
If f'(x) is above the x-axis, it means that the slope of f(x) at x is positive. And when the slope of a function is positive at a given point, it means that the function is increasing at that point.
Therefore, in this case, we can conclude that the function f(x) is increasing at x=2, since the graph of f'(x) is above the x-axis at that point.
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