Question

suppose f(x) is continuous and that f(-5)=2, f(0)=-3. f(3)=2, f(7)=-4, f(8)=-1.Which smallest interval where f (x)= 0 is guaranteed to have a solution: [-5,0], [0,3], [3,7], or [7,8]?

Answer 1

Answer:

[0,3]

Step-by-step explanation:

Using a special case of mean value theorem, The Intermediate Zero Theorem:

if sign changes in continuous function, it pass through zero:

f(-5)=2, f(0)=-3. f(3)=2, f(7)=-4, f(8)=-1

[-5,0], [0,3], [3,7] guarantee a solution

smallest : [0,3]