When f ‘(x) changes fro positive to negative, f(x) has a
relative maximum
local maximum at that point.
When a function’s derivative changes from positive to negative at a certain point, it means that the function is increasing up until that point and decreasing after that point; this implies that the function has reached a maximum point at that location. This is because as the function’s slope changes from positive to negative, the tangent line to the curve changes from upward sloping to downward sloping, indicating a change in direction from moving up to moving down.
Therefore, we can conclude that when f ‘(x) changes from positive to negative, f(x) has a local maximum at that point. It is important to note that the local maximum may not necessarily be the overall maximum of the function if there are other local maxima present.
More Answers:
The Instantaneous Rate Of Change: An Alternate Definition Of DerivativesMaster The Fundamentals: The Limit Definition Of Derivative In Calculus
Increasing F'(X) And Its Effect On The Curve Of F(X)