Question

Prove that the function f(x) = 3x^4 +12x-19 must have at least one real zero on the interval (0,3)

Answer 1

Can you tell me what the value of `f(0)` is?

Answer 2

-19?

Answer 3

yes, now how about `f(3)` ?

Answer 4

260

Answer 5

notice how we change from negative to positive

-19 to +260

Answer 6

since y changes sign, this means that y has to be 0 at some point (at least once) in the interval