Thanks, speed will be appreciated QUESTION 2Mark all true statements (there might be more than one statement that is true).Suppose that f and its first n derivatives are continuous on [a, b], differentiable on (a,b) and x € [a, b]. Then for each x € [a, b], there is c in the interval with the endpoints x and x, such thatE00f'(xo)f''(xo)(n) (x₂)f(n+1)¹) (c)(n+1)!·(x-x₂).1!2!n!Suppose that f is differentiable on an interval (a,b). If f is not injective on (a,b), then there exists a point c = (a, b) such that f'(c) = 0.x³sin-(+²+(1)X0f(x) = f(x) +· (x − x) +A function f: ACR→R given by f(x) =(X-X '++fif x # 0· ( x − x₂) ¹ +is a class ² function on R.n+1if x=0Let f:R→R be given by f(x) = |x|³. Then ƒ is a class 6¹ function on R.1○ Let f: (a, b) → R be differentiable on (a, b). Then f'(x) > 0 for all x € (a,b) if and only if f is strictly increasing.

We have to identify the true statements from the given statements.

Mark all true statements (there might be more than one statement that is true). 0 Suppose that f and its first derivatives are continuous on [a, b], differentiable on (a,b) and x € [a, b]. Then for each x = [a, b], there is c in the interval with the endpoints x and x, such that 0 f'(xo). f(n) (xo) -(x-x)²+...+ (x-x)"+ f(n+1) (c) (n+1)! (x-x)+1 1! n! Suppose that f is differentiable on an interval (a,b). If f is not injective on (a, b), then there exists a point c E (a, b) such that f'(c) = 0. (-) f(x)=f(x) + -(x-x)+ f'(xo) 2! 0 A function f: ACR→R given by f(x) = x³sin if x # 0 is a class 2 function on R. 0 if x=0 Let f:R→R be given by f(x) = |x|³. Then f is a class ¹ function on R. Let f: (a, b) → R be differentiable on (a, b). Then f'(x) > 0 for all x € (a,b) if and only if f is strictly increasing.

Mark all true statements (there might be more than one statement that is true). 0 Suppose that f and its first derivatives are continuous on [a, b], differentiable on (a,b) and x € [a, b]. Then for each x = [a, b], there is c in the interval with the endpoints x and x, such that 0 f'(xo). f(n) (xo) -(x-x)²+...+ (x-x)"+ f(n+1) (c) (n+1)! (x-x)+1 1! n! Suppose that f is differentiable on an interval (a,b). If f is not injective on (a, b), then there exists a point c E (a, b) such that f'(c) = 0. (-) f(x)=f(x) + -(x-x)+ f'(xo) 2! 0 A function f: ACR→R given by f(x) = x³sin if x # 0 is a class 2 function on R. 0 if x=0 Let f:R→R be given by f(x) = |x|³. Then f is a class ¹ function on R. Let f: (a, b) → R be differentiable on (a, b). Then f'(x) > 0 for all x € (a,b) if and only if f is strictly increasing.

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

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