Using the results from the previous section, we are now able to determine whether a critical point of a function actually corresponds to a local extreme value. In this section, we also see how the sec...Using the results from the previous section, we are now able to determine whether a critical point of a function actually corresponds to a local extreme value. In this section, we also see how the second derivative provides information about the shape of a graph by describing whether the graph of a function curves upward or curves downward.
let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive ...let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive to negative as x increases through c, then f has a local maximum at c; if f′ changes sign from negative to positive as x increases through c, then f has a local minimum at c; if f′ does not change sign as x increases through c, then f does not hav…
