If f(x) is increasing, then f'(x) is?
If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase
If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase. Mathematically, this can be represented as:
if x₁ < x₂, then f(x₁) < f(x₂) The derivative of a function, f'(x), represents the rate of change or the slope of the function at any given point. Therefore, if f(x) is increasing, it means that the function is getting steeper as x increases. When f(x) is increasing, f'(x) is positive. This indicates that the slope of the function at any point is positive, meaning that the function is becoming steeper or increasing at that particular point. In summary, if f(x) is increasing, then f'(x) is positive, indicating that the slope of the function is positive, and the function is becoming steeper as x increases.
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