Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval.y = sin(x³), (1, 2)Let f(x) = sin(x³). Then f is continuous 0, then substituting the value A found above and simplifying, f(A) = sinsuch that f(c) = f(d) =Thus, f has at least two x-intercepts in (1, 2).Read ItXXfor n in Z, so we note that< 0, and f(2)=sin(8) > 0. Applying the intermediate value theorem on [1, A] and then on [A, 2], we see there are numbers c and d in (1, A) and (A, 2),

Answered: Image /qna-images/answer/36b38bce-bc8a-46fd-9134-3cd67d2e1259.jpg

Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval. y=sin(x³), (1, 2) Let f(x)=sin(x³). Then fis continuous ✔✔✔ on the interval [1, 2] since fis the composite of the sine function and the cubing function, both of which are continuous ✔✔✔ on R. The zeros of sin(x) are at x - 0 <1 <# 3³ <2m <8 < 3m. Applying the intermediate value theorem and taking the pertinent cube roots these values in the inequality, we have the following. [call this value A] < 2 1<√ 01<√3 [call this value A] 0, then substituting the value A found above and simplifying, f(A)=sin( such that f(c) f(0) = Thus, f has at least two x-intercepts in (1, 2). Need Help? Read It x forn in Z, so we note that < 0, and f(2)=sin(8) > 0. Applying the intermediate value theorem on [1, A] and then on [A, 2], we see there are numbers c and d in (1, A) and (A, 2),

Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval. y=sin(x³), (1, 2) Let f(x)=sin(x³). Then fis continuous ✔✔✔ on the interval [1, 2] since fis the composite of the sine function and the cubing function, both of which are continuous ✔✔✔ on R. The zeros of sin(x) are at x - 0 <1 <# 3³ <2m <8 < 3m. Applying the intermediate value theorem and taking the pertinent cube roots these values in the inequality, we have the following. [call this value A] < 2 1<√ 01<√3 [call this value A] 0, then substituting the value A found above and simplifying, f(A)=sin( such that f(c) f(0) = Thus, f has at least two x-intercepts in (1, 2). Need Help? Read It x forn in Z, so we note that < 0, and f(2)=sin(8) > 0. Applying the intermediate value theorem on [1, A] and then on [A, 2], we see there are numbers c and d in (1, A) and (A, 2),

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

See similar textbooks