For the given function, determine consecutive values of x between which each real zero is located. f(x) = –14x4 – 7x3 – 18x2 + 17x + 11

[0,1] and [-1,0]

Step-by-step explanation:

We have the function to determine consecutive values of x between which each real zero is located we have to replace the function with different values and then analyze the results.

We are going to replace the function with x=0,

Now we are going to replace with x=1,

With x=2,

Now with x=-1,

With x=-2,

We have to analyze:

We have that f(2) and f(1) have the same signs both are negatives this means that there isn't a zero between the interval [1,2].

We have that f(1) and f(0) have opposite signs this means that there is a zero between the interval [0,1].

f(0) and f(-1) have opposite signs too, then there's also a zero in the interval [-1,0].

And finally, f(-1) and f(-2) have the same signs then there isn't a zero in the interval [-2,-1]

The graph of the function shows that the answer is correct: