i am wondering if the following answer to my math problem is correct

f(x)=x^3-4x-2 [2,3]

the answer i put was f(20<o and f(3)>0

What is the meaning of the [2,3] after the definiton of f(x) ?

f(3) = 27 -12 -2 = 13

Why are you calculating f(20) ?

what are prime numbers

To check if your answer for the given math problem is correct, we need to determine the sign of the function at the given values. Here's how you can find the solution and verify your answer:

1. Start by plugging in the first value given, x = 2:
f(2) = (2)^3 - 4(2) - 2
= 8 - 8 - 2
= -2
So, f(2) = -2.

2. Next, substitute the second value, x = 3:
f(3) = (3)^3 - 4(3) - 2
= 27 - 12 - 2
= 13
Hence, f(3) = 13.

Now, let's analyze the results.

You mentioned that your answer was f(20<o and f(3)>0.

It seems there might be a slight typo as it's unclear what you meant by "20<o." However, let's evaluate f(20) and infer the information based on the results.

3. Evaluate the function at x = 20:
f(20) = (20)^3 - 4(20) - 2
= 8000 - 80 - 2
= 7918
Thus, f(20) = 7918.

From the calculations, we can summarize the following information:

a) f(2) = -2
b) f(3) = 13
c) f(20) = 7918 (based on an assumption related to your answer)

Since both f(2) and f(20) are negative (or zero) and f(3) is positive, we can conclude the following:

- The function f(x) is negative (or zero) for x values between 2 and 20.
- The function f(x) is positive for the value x = 3.

Therefore, based on this analysis, your answer appears to be correct.