Question

Use the intermediate value theorem to show that the polynomial has a real zero between the given integers. f(x) = 4x3 - 2x - 5; between 1 and 3 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Simplify your answers.) A. Because f(x) is a polynomial with f(1) = <0 and f(3) = <0, the function has a real zero between 1 and 3. B. Because f(x) is a polynomial with f(1) = <0 and f(3) = >0, the function has a real zero between 1 and 3. OC. Because f(x) is a polynomial with f(1) = >O and f(3) = <0, the function has a real zero between 1 and 3. D. Because f(x) is a polynomial with f(1) = >O and f(3) = > 0, the function has a real zero between 1 and 3.

Answer 1

Solution:- Intermediate mean value theormistates that it f is a continuous function whose domain contains the interval Caib) then it takes on any given value between fra) and f(b) at some point within the interval. j.e. let s be a number with fraj is cf(b) then there esist somie between that a and b such x flie) ES is continuous function Given fcre) = 483-zx-5 (: Polynomial function is continuous everywhere on (-00,00)) let S=0 fla) fuil = 41103-2-1)-5 = 4-7 = fch) = f(8) = 4(3) 3 -263) -5 = 108 -11 = 97 fla) < s < flb) 3 <0. < 97 so using theorm there exist de E Carb) such that fcde) = 0 Answer: option B] Because flue) is a polynomial with f(1) = 3 Lo and f(3) = 9770, the function has a real zero between i and 3.