Question

estion 8 Which one of the following functions satisfies the hypotheses of Rolle's Theorem in the interval [-1, 1] aswer saved arked out of 2.00 Select one: o a. f(x)=x2-x). Flag question 1 b. f(x) ? 4 1 O c. f(x) = 1 d. f(x) = -2

Answer 1

solution - The Rolles theorem to lea following satisfied states that the closed in general must be In the 1) f(x) is continuous on interval [ab] open internal (a, b) is differentiable 3). O = 10 Now, we have a) fina - 1x in [-1,1 flip The function does not have any point inside the internal a (-1; 1) at which fails here (-1, 1) derivative is equal to o The Rolle's Theorem bооцоо, f(x) is not diffent over the whole internal

(6) f(x) = x² - 1 x2 - 4 in [-1,1 The function 'f' is continuous in the interval [11] and differentiable on the open internal (-1, 1). The denvative is defined. Also fZ-1) = (1-12 O (1) 2 - 4 O I-4 And f 0 = = f(-1) = f (1) is satisfied so, all the 3 conditions of Rolle's Theoren is satisfied © in (11 The functions, the function is not diff. x2 at f(u) = -1 The function is not continuous Rolle's ferentiable in [-21 Theorem is not applicable here f(n) = x-x in C-1, 1 The function of is (d) is continuous