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\fSuppose that for a function f, f(6) is not defined. Also suppose that lim f(x) = -3 and lim f(x) = -3. Which, if any, of the following statements a) through d) are false? x-+6- x-6+For which of the following functions can we use the Intermediate Value Theorem to prove the existence of roots in the indicated interval? 1. f(x)="'2 a [25 2] 11. f(x) = x2 + 7, [2, 2] III. f(x) = 2x3 7x, [2, 2] x+1 x4' Iv. f(x) = [2, 21 Suppose that f(x) is a continuous function on x E [-4, 4],and f(-4) = 3, f(4) = 8. By the Intermediate Value Theorem, which of the following is guaranteed to be true?Given f(x) = 7 cos(3 x) , which of the following expressions will represent the first step when finding f ' (x) using the definition of derivative? a) O (7 cos(3 (x + h))) - (7 cos(3 x)) h b) O lim (7 cos(3 (x + h))) - (7 cos(3 x)) h-0 h c) O lim (7 cos(3 (x + h))) - (7 cos(3 x) ) x-h h d) O lim (7 cos(3 x) + h) - (7 cos(3 x)) h-0 h e) O lim 7 cos(3 (x + h)) h-0 h f) O none of these.Find A and B given that the function, f(x), is differentiable at x = 1. f (x ) = x2 + 5 x