(a) Esboce o gráfico de uma função cm[-1,2] que tenha máximo absoluto, mas nâo tenha máximo loca

step 1 So we want to sketch a graph from negative 1 and 2 that will say have an absolute max but no loc

(a) Esboce o gráfico de uma função cm[-1,2] que tenha máximo...

(a) Esboce o gráfico de uma função $\mathrm{cm}[-1,2]$ que tenha máximo absoluto, mas nâo tenha máximo local.
(b) Esboce o grafico de uma funçiso $\mathrm{em}[-1,2]$ que tenha um máximo local, mas não tenha máximo absoluto.

Key Concepts

Absolute Maximum

An absolute maximum is the highest value a function attains on its domain. It is defined as a point where the function's value is greater than or equal to the function values at every other point in the domain, regardless of the proximity of those points.

Local Maximum

A local maximum is a point in the domain where the function's value is higher than or equal to the values at all nearby points. Unlike an absolute maximum, a local maximum only provides a comparative high value within a small neighborhood around the point, not over the entire domain.

Continuity

Continuity is a property of a function where small changes in the input result in small changes in the output, ensuring that the graph of the function does not have any breaks or jumps. In the context of finding extrema, continuity on a closed interval guarantees the existence of both absolute maximums and minimums.

Endpoint Consideration

When dealing with functions defined on closed intervals, endpoints are important in determining absolute extrema. Even if an endpoint does not have a local maximum characteristic (due to the absence of a neighborhood on one side), it can still serve as the absolute maximum of the function.

Graph Sketching

Graph sketching involves drawing a function's behavior over a given domain to visually identify features such as absolute and local extrema. This process helps illustrate the distinction between overall extrema and those that occur only within a local neighborhood.

Transcript

Please give Ace some feedback