Use the intermediate value theorem to determine whether the

Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]

a. f(-1) = -16 and f(0) = -5; no

b. f(-1) = -16 and f(0) = 5; yes

c. f(-1) = 16 and f(0) = -5; yes

d. f(-1) = 16 and f(0) = 5; no

Solution

f(x) = 8x^3 - 10x^2 + 3x + 5

f(-1) = 8(-1)^3 - 10(-1)^2 + 3(-1) + 5 = -16

f(0) =  8(0)^3 - 10(0)^2 + 3(0) + 5 = 5

So yes

b. f(-1) = -16 and f(0) = 5; yes