i am wondering if the following answer to my math problem is correct
f(x)=x^3-4x-2 [2,3]
We are doing limits and are suppose to use the Intermediate value thereom
the answer i put was f(2)<o and f(3)>0
what are the multipuls of 15
30 45 60 75 90 105 so on
help with my problem!!!
i am not sure how the multiples of 15 come into this problem?
lol u ppl are funny u know there is such a thing as "post new question" at the top of the page not sure if u spotted it ppl are less likely to answer ur question if u post on other ppl's questions.
To determine if your answer is correct using the Intermediate Value Theorem, you need to check if the function value changes sign between the given interval [2, 3]. Here's how you can verify it step by step:
1. Calculate the function value at the lower endpoint, f(2):
f(2) = (2^3) - (4*2) - 2
f(2) = 8 - 8 - 2
f(2) = -2
2. Calculate the function value at the upper endpoint, f(3):
f(3) = (3^3) - (4*3) - 2
f(3) = 27 - 12 - 2
f(3) = 13
3. Now, check if the sign of f(2) is less than 0 and the sign of f(3) is greater than 0. Based on your answer, you should have f(2) < 0 (which is correct) and f(3) > 0 (which is also correct).
Since the function changes sign from negative to positive within the interval [2, 3], the Intermediate Value Theorem guarantees the existence of at least one (and possibly more) root within that interval.
So, based on your answer, f(2) < 0 and f(3) > 0, it seems like you are correct. The Intermediate Value Theorem supports the existence of a root for the function f(x) = x^3 - 4x - 2 within the interval [2, 3].