the slope of f'(x) is positive at x=2
f(x) is concave up when x=2
If the slope of f'(x) is positive at x=2, it means that the function f(x) is increasing at x=2. This can be explained as follows:
The derivative of a function f(x) at a point x gives the slope of the tangent line to the graph of the function at that point. If the slope of f'(x) is positive at x=2, it means that the tangent line to the graph of f(x) at x=2 has a positive slope.
In other words, as we move from left to right along the x-axis and approach x=2, the value of the function f(x) is increasing. This suggests that the function is trending upwards near x=2.
For example, if f(x) represents the height of a plant over time, and x=2 corresponds to a certain day, then a positive slope of f'(x) at x=2 means that the plant is growing taller on that day.
To summarize, when the slope of f'(x) is positive at x=2, it indicates that the function f(x) is increasing (or trending upwards) at that point.
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