For fx x3 2x3 x 4 use the Intermediate Value Theorem to

For f(x) = x^3 + 2x^3 - x - 4, use the Intermediate Value Theorem to determine which interval must contain a zero of f. A. Between -1 and 0 B. Between 0 and 1 C. Between 1 and 2 D. Between 2 and 3

Solution

Given

f(x) = x^3 + 2x^2 + x - 4

If the function is negative and then becomes positive it must pass through zero.

Now f(-1) = (-1)^3 + 2(-1)^2 + (-1) - 4 = -4

f(0) = (0)^3 + 2(0)^2 + (0) - 4 = -4

f(1) = (1)^3 + 2(1)^2 + (1) - 4 = 0

f(2) = (2)^3 + 2(2)^2 + (2) - 4 = 14

f(3) = (3)^3 + 2(3)^2 + (3) - 4 = 44

So option B) is correct.