Find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. Donot graph.f(x) = 2x +128XSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The critical number(s) is(are)(Type integers or simplified fractions. Use a comma to separate answers as needed.)B. The function has no critical numbers.

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Answered: Find the critical numbers, the…

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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Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = 4x² - 16x +4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function is increasing on (Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.) B. The function is never increasing.
Determine the intervals on which the function is concave up or down and find the points of inflection. f(x) = 6x³ - 5x² + 1 (Give your answer as a comma-separated list of points in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which f is concave up. (Give your answer as an interval in the form (*, *). Use the symbol ∞o for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E Determine the interval on which f is concave down. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty.…
a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x²-50x² +625 a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function f is increasing on the open interval(s) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function f is decreasing on the open interval(s) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) OB. The function is never…
Determine the intervals on which the function is concave up or down and find the points of inflection. f(x) = 6x³ - 11x² + 1 (Give your answer as a comma-separated list of points in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: DNE Incorrect Determine the interval on which f is concave up. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) XE ( + 1,00) Determine the interval on which f is concave down. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the…
Find the intervals on which the graph off is concave upward, the intervals on which the graph off is concave downward, and the inflection points. 1(x) = -x + 12x³-12x+5 For what interval(s) ofx is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) OB. The graph is never concave upward.
Find the domain and the range of the following function. x+ 3, for x or f(x) = O B. ff(x) I f(x) s or f(x)= or f(x) 2 O c. ffx) I f(x) or f(x) 2 or f(x) = O D. ff0x) I f(x) f(x)= or f(x)> or

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