the function f is decreasing/- slope then f'(x) would be
If the function f is decreasing, it means that as the input value x increases, the corresponding output values f(x) are decreasing
If the function f is decreasing, it means that as the input value x increases, the corresponding output values f(x) are decreasing. Mathematically, we can say that the function f(x) has a negative slope.
In calculus, the derivative of a function measures its rate of change at any given point on its graph. So, if f is a decreasing function, then its derivative f'(x) should reflect this behavior.
The derivative of a function can be thought of as the slope of its tangent line at a particular point. When the function is decreasing, the slope of the tangent line must be negative.
Therefore, if f is a decreasing function, the derivative f'(x) would be negative or less than zero for all x in the domain of the function.
In notation, we would write: f'(x) < 0 for all x ∈ Domain of f.
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