Use the intermediate value theorem to show that f(x) = -x^4 + 3x^3 - 2x + 1 has zero between 2 and 3

I did

a=2, b=3

so

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

= -16 + 24 - 4 + 1

= -20 + 25

= 5

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

= - 81 + 81 - 6 + 1

= -87 + 82

= -5

Is this correct?