Find the absolute maximum and minimum values of the function: F(x) = ln(x) on the interval [1,3]...

Question:

Find the absolute maximum and minimum values of the function:

{eq}F(x) = \ln(x) {/eq} on the interval{eq}[1,3] {/eq}

- Show domain of the function

- {eq}x {/eq} and {eq}y {/eq} intercepts

- Find any asymptotes

- Find local max and min values where {eq}f {/eq} is increasing or decreasing

- Show concavity and inflection points.

Definitions

Absolute maximum and minimum values of the function: Point where the function achieves its maximum or minimum value of all the point given in the domain.

Domain of the function : Range in which function takes values.

Asymptotes : A straight line that continually approaches a given curve but does not meet it at any finite distance.

Local max and min values : Maximum value a function take in a certain small interval.

Concavity : A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point and concave down at a point if the tangent line lies above the graph in the vicinity of the point.

Inflection Point : Point where the graph changes its curvature

Answer and Explanation:

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F'(x) = 1/x which is always positive in the given domain.

F"(x) = {eq}-1/x^2 {/eq} which is always negative in the given domain

So maximum and...

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