Concluded

Definition

When we conclude something about $h(x)$ at $x = l$ based on information about its first derivative changing from positive to negative, it means we make an inference or deduction about certain characteristics or behavior of $h(x)$ at that specific point.

Related terms

Monotonicity: Monotonicity refers to whether a function is always increasing, always decreasing, or neither over an interval. The sign change in the first derivative indicates potential monotonic behavior changes.

Concavity:

Concavity describes whether a curve opens upward (like U) or downward (like n). The first derivative sign change can suggest a change in concavity.

Increasing/Decreasing: These terms describe the behavior of a function as it moves from left to right. A change from positive to negative indicates a transition from increasing to decreasing.