7. Show that the function r(0) = 0+ sin2 -8 has exactly one zero in the interval (-o,00). Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a) = f(b), then there is at least one number c in (a,b) at which f (c) = 0. Find the derivative of r(0) =0 + sin2 -8. r'(0) = Can the derivative of r(0) be zero in the interval (-0,0)? O Yes O No in the interval (-0,00). According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1) Which theorem can be used to determine whether a function has any zeros in a given closed interval? O A. Mean value theorem O B. Extreme value theorem OC. Intermediate value theorem

7. Show that the function r(0) = 0+ sin2 -8 has exactly one zero in the interval (-o,00). Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a) = f(b), then there is at least one number c in (a,b) at which f (c) = 0. Find the derivative of r(0) =0 + sin2 -8. r'(0) = Can the derivative of r(0) be zero in the interval (-0,0)? O Yes O No in the interval (-0,00). According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1) Which theorem can be used to determine whether a function has any zeros in a given closed interval? O A. Mean value theorem O B. Extreme value theorem OC. Intermediate value theorem

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Description: Can i get help step by step? 7.Show that the function r(0) = 0+ sin2-8 has exactly one zero in the interval (-o,00).Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

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Question

Can i get help step by step?

7.
Show that the function r(0) = 0+ sin2
-8 has exactly one zero in the interval (-o,00).
Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a) = f(b), then there is at least one number c in (a,b) at which f (c) = 0.
Find the derivative of r(0) =0 + sin2
-8.
r'(0) =
Can the derivative of r(0) be zero in the interval (-0,0)?
O Yes
O No
in the interval (-0,00).
According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval (- 0,00), there cannot be two points e= a and 0=b for which r(a) =r(b) in this interval. In other words, the function r(0) has (1)
Which theorem can be used to determine whether a function has any zeros in a given closed interval?
O A. Mean value theorem
O B. Extreme value theorem
OC. Intermediate value theorem

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