use the intermediate value theorem to show the polynominal function has a zero in the given interval

Question

f(x)=x^5-x^4+3x^3-2x^2-11x+6; [1.5,1.9]

x= -2.33

y=10.19

after i plugged in the 1.5 and 1.9 i just want to know if my x and y are correct

Answer 1

i changed it too

f(1.9)= 10.186

f(1.5)= -2.344

Answer 2

so, the IVT says that if f(x) is continuous, it must take on all values between 10.186 and -2.344.

That includes 0, so there is the proof.

BTW, you values for f are correct.

Answer 3

so i am right? x and y?
x=-2.344
y=10.186

it was continuous, but they wanted it rounded to three decimal places

Answer 4

I wouldn't call your values x and y.

You have two x-values: 1.5 and 1.9
and two values for f(x) or y: -2.344 and 10.186

and, as I said, given those two values for x, your two y values are correct to 3 places.