Given the Graph of Y = F (X), Answer the Following

question 51

Essay

Given the graph of y = f (x), answer the following questions. Find all values of x at which
(a) $f ^ { \prime } ( x ) > 0$ (b) $f ^ { \prime } ( x ) < 0$ (c) $f ^ { \prime } ( x ) = 0$ (d) f is increasing.(e) f is decreasing.(f) $f ^ { \prime \prime } ( x ) > 0$ (g) $f ^ { \prime \prime } ( x ) < 0$ (h) f has an inflection point.(i) $f ^ { \prime } \text { is increasing. }$ (j) $f ^ { \prime } \text { is decreasing. }$

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Definitions:

Forward Direction

In the context of a chemical reaction, refers to the progression of reactants to form products, as opposed to the reverse process.

Hexanoyl Chloride

An organic compound used as a reagent in organic synthesis, characterized by a six-carbon chain ending with a carbonyl chloride functional group.

Dimethylamine

A simple organic compound that consists of nitrogen attached to two methyl groups.

Mechanism

A detailed description of the step-by-step process by which a chemical reaction occurs, including the breaking and formation of bonds.