Question

1.Use the IVT to explain why the following is true. If f continuous on (a,b) and f(x) does not equal to zero for all x in the interval (a,b), then f(x) > for all x in the interval (a,b) or f(x) < 0 for all x in the interval (a,b).

2. You are given that a function f is defined and continuous at every real number x except x=2. Also, f(x)=0 precisely for x=1 and 7. Finally, you know that f(-3)=4, f(1.5)=2, f(4)= -3, and f(10)=6. Solve the inequality f(x) > 0.