2. Determine whether Rolle's Theorem applies to the function f(x) = x(x - 1)?: [0,1]
Determine whether Rolle's Theorem can be applied to f(x) = cos(x) + sin(x) on the interval (7/2, 7)? If so, find the point(s) guarenteed to exist by Rolle's Theorem. [6]
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.)f (x) = sin(x), [0, 2π]If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)I thought the derivative would be cos(x) so then cos(0) would be 1 but thatz wrong so now I don't understand...
3 (as state Rolle's Theorem and apply it for (3pts) the function f(x) = 4x-x² on interval [0,47 (b) State mean Value Theorem and apply it for the function g(x) = 6x² on the interval [1, 2] (3 pts)
2. Rolle's theorem states that if F : [a, b] → R is a continuous function, differentiable on Ja, bl, and F(a) = F(b) then there exists a cela, b[ such that F"(c) = 0. (a) Suppose g : [a, b] → R is a continuous function, differentiable on ja, bl, with the property that (c) +0 for all cela, b[. Using Rolle's theorem, show that g(a) + g(b). [6 Marks] (b) Now, with g still as in part (a),...
2. The function (-3x if 0sx < 1 if x 1 -fO f(x) =f(x) 0 Is zero at x 0 and x = 1 and differentiable on (0,1), but its derivative on (0,1) is never zero. Does this example contradict Rolle's Theorem? Why or why not?
2. The function (-3x if 0sx
a. Determine whether the Mean Value Theorem applies to the function f(x) = x + on the interval [3,5). b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem. a. Choose the correct answer below. O A. No, because the function is continuous on the interval [3,5), but is not differentiable on the interval (3,5). OB. No, because the function is differentiable on the interval (3,5), but is not continuous on the...
how do i solve this with Mean Theorem Value?
4. 0.5/1 poilnts 1 Previous Anawars LarCal: 11 3.2 020 Determine whether Rolle's Theorem can be applied to f on the closed interval bl. (select all that apply.) Yes O No, because fis not continuous on the closed Interval [a, bl ND, hecause fis rnot differentiable in the open interval (a, b). No, because ) If Ralle's Theorem can be applied, find all values of cin the open interval (a, b)...
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
Verify that Rolle's Theorem can be applied to the function f(x) = -10 + 310 - 30 on the interval 2,5). Then wyd all Question 1: (6 points) values of c in the interval such that f'(c) - 0. Enter the exact answers in increasing order. To enter a type sqrt(a). Please explain, in your own words and in a few sentences, how you arrived at your answers.
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2 – 24x + 2x2, [5, 7]