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Complete parts (a) through (c) for the following function. f(x)=-3x³ +6x². - 4x-5 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable.

Complete parts (a) through (c) for the following function. f(x)=-3x³ +6x². - 4x-5 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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q28-h8. Do parts A & B & C

Complete parts (a) through (c) for the following function. f(x) = − 3x³ + 6x² - 4x-5 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. (a) Find intervals where the function is increasing or decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function is increasing on and decreasing nowhere. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) B. The function is increasing on and decreasing on (Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed. Type your answers in interval notation.) C. The function is decreasing on and increasing nowhere. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) D. The function does not increase or decrease on any interval.
Transcribed Image Text:Complete parts (a) through (c) for the following function. f(x) = − 3x³ + 6x² - 4x-5 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. (a) Find intervals where the function is increasing or decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function is increasing on and decreasing nowhere. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) B. The function is increasing on and decreasing on (Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed. Type your answers in interval notation.) C. The function is decreasing on and increasing nowhere. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) D. The function does not increase or decrease on any interval.
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