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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View this answerF'(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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