Let f be the function given by f(x) = x+ tan(x/5) -10. The intermediate Value Theorem applied to f on the close interval [12,15] guarantees a solution in [12,15] to which of the following equation?

Question

Let f be the function given by f(x) = x+ tan(x/5) -10. The intermediate Value Theorem applied to f on the close interval [12,15] guarantees a solution in [12,15] to which of the following equation?

1) f(x) = -10

2) f(x) = 0

3) f(x) = 4

4) f(x) = 14

HELP HELP HELP

Answer 1

Well f(12) = 21.16

f(15) = 4.85

f(x) is continuous on the interval

So if 4.85 < y < 21.16 the IVT says there is an x in the interval [12,15] so that f(x) = y

So the answer is (4)