the function f is increasing/+ slope then f'(x) would be
If the function f is increasing, it means that as x increases, the corresponding values of f(x) also increase
If the function f is increasing, it means that as x increases, the corresponding values of f(x) also increase. In terms of the slope of the graph of f(x), this indicates that the slope is positive throughout the domain.
If we want to express this idea using calculus, we can consider the derivative of the function f'(x). The derivative of a function represents its rate of change or the slope of the tangent line to the graph of the function at any given point.
Since we are given that f is increasing, this indicates that f'(x) > 0 for all values of x in the domain. In other words, the derivative of f(x) is positive everywhere. This tells us that the graph of f(x) is always sloping upward (has a positive slope), reinforcing the notion that the function is increasing.
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