consider the function f(x) = x3 / x2 - 1 .We have f'(x) = x2(x2-3) / (x2-1)2 and f"(x) = 2x(x2+3) / (x2-1)3 1. Using a table, show where f is increasing or decreasing, and where f is concave up or concave down. Specify in the table all relative minimum points, relative maximum points, and points of inflection of the graph of f. 2. Sketch the graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with
consider the function f(x) = x3 / x2 - 1 .We have f'(x) = x2(x2-3) / (x2-1)2 and f"(x) = 2x(x2+3) / (x2-1)3 1. Using a table, show where f is increasing or decreasing, and where f is concave up or concave down. Specify in the table all relative minimum points, relative maximum points, and points of inflection of the graph of f. 2. Sketch the graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with
consider the function f(x) = x3 / x2 - 1 .We have f'(x) = x2(x2-3) / (x2-1)2 and f"(x) = 2x(x2+3) / (x2-1)3 1. Using a table, show where f is increasing or decreasing, and where f is concave up or concave down. Specify in the table all relative minimum points, relative maximum points, and points of inflection of the graph of f. 2. Sketch the graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with
consider the function f(x) = x3 / x2 - 1 .We have f'(x) = x2(x2-3) / (x2-1)2 and f"(x) = 2x(x2+3) / (x2-1)3
1. Using a table, show where f is increasing or decreasing, and where f is concave up or concave down. Specify in the table all relative minimum points, relative maximum points, and points of inflection of the graph of f.
2. Sketch the graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with their equations.
Transcribed Image Text:x²(r² – 3)
(r2- 1)2
2.x (x2+3)
(22 - 1)3
1. Consider the function f(r) =
We have f'(r) =
1
and f"(r)
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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