Question

4. The function f is continuous on the closed interval (-2, 1). Some values of f are shown in the table below. --2 f(x) -3 -1 0 1 7 k3 The equation f(x) = 3 must have at least two solutions in the interval [-1,1) if k = a. 1 b. C. 2 CONN NICO d. 5. If k(r) is a continuous function over the interval (-2, 4) such that k(-2) = 3 and k(4) = 1, then k(2) 0 must have a solution inside the interval (-2,4) by the Intermediate Value Theorem. TRUE FALSE 6. Let S (2) be a continuous function with the following known values. -4 --2-1 2 57 1 1 (2) -5 -1 1 -3 48 (a) What is the minimum number of zeros that f() must have? Justify your answer. (b) Does f(x) = - have a solution? Justify your response.

Answer 1

4. If k=1 ,then f will attain every value between 7 and 1.Also f attains every value between 1 and 3.It means f attains value 3/2 twice in interval (-1,1). 5.False.As k(-2)=3 and k(4)=1 both are positive so k may or may not cross x axis. 6(a).From the given table we see f changes its sign thrice.So f has atleast 3 zeros. (b).As f(-4)=-5, f(-2)=-1 and f is continuous so f will attain every value between -5 and -1.It means f attains - 7/2 once in (-4,-2).This f (x)=-7/2 has a solution.