Question 4 Rolle's theorem states that if a function fis continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f(x) = 0 for some x with a sxsb. (A) True B) False

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 => x = 0 and y = 0

Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: True f must be continuous in its domain? or false: If f(x) is differentiable in its domain then

A:

Q: lim 3i 4 +

A:

Q: If a function f(x) is not defined at x-a, then it is not continuous at an open interval (a, b) * O…

A: Given Statement is "False"

Q: Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a…

A: Given function f(x)=|x|interval [-2,2] We apply Rolle's theorem only when the function is continuous…

Q: Function g: R → R, defined by g(x) = x" +5 is a one-to-one function. O True O False QUESTION 8…

A:

Q: 10) The function f below satisfies Rolle's Theorem in the interval [a, b] because (a) f is…

A: Rolle's Theorem