Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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For a rational function R, if the degree of the numerator is
less than the degree of the denominator, then R is ________.
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- Find all the rational zeros of the function. x³ - 18x² + 108x - 216 O -6 0, -1 0,6 6 ±6arrow_forwardThe time in seconds, t, it takes for a specific object being dropped from a particular height in feet above sea level, h, to reach the ground can be found by the radical function -√. At what height should you drop an object in order for it to reach the ground in 12 seconds? O 9 feet O 36 feet O 96 feet O2,304 feetarrow_forwardDetermine 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…arrow_forward
- If the remainder is zero (0) when f(x) is divided by x-4, this means that x-4 is a ____arrow_forward3. For the function f(x) = 2x4 – 5x3 + 9x² + x – 15: a. State the degree of the polynomial b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to find all of the possible rational zeros d. Look at the graph or Table on a graphing calculator to determine which numbers on the list of rational zeros are real zeros indicated by the x-intercepts of the graph. In the space below, use synthetic division to verify one rational zero. Note: If the division remainder is zero, the number divided is a zero of the function. е. f. Find all remaining zeros. (Show work!) Note: Use the reduced polynomial (the quotient from the division) to continue the search for zeros © If the degree of the reduced polynomial is higher than 2, continue the synthetic division process with another real zero. (Remember: a number may be a multiple zero – i.e. occur more than once ) © Whenever the reduced polynomial is quadratic, the zeros can be found by using methods for…arrow_forwardf(x) = - 9(x - 5)(x+ 9)² (a) Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The real zero(s) of f is/are (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.'arrow_forward
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