Intermediate value theorem

 

If f is continuous on [a, b]. Then f takes all values between f(a) and f(b).

If it is the case that the signs of f(a) and f(b) are the same, does that mean the function f(x) cannot have a zero between a and b? Explain.

A zero will be between a and b if the signs of f(a) and f(b) are opposite.

If same sign, it does not mean they cannot have a zero between a and b.

 

f(x) = (x-1)(x-2), and a = -10, b=10

f(-10)>0, f(10)>0, but there are two zeros between -10 and 10

We have on negative and one positive number for ‘x’ f(-10)>0, f(10)>0.

 

Instructor reply:

Thanks for your post. I appreciate your hard work discussing about the zero of polynomial. However, it seemed to have been almost word for word from a source on the internet. Please know that your posts must be in your own words, and if you use a source you need to cite it. Also please make sure the example you provided is original as well in order to demonstrate your understanding. Please return to the discussion board and revise your post to receive credit for this week’s discussion.

 

Try to further explain how to find f(-10) and f(10)? How to find the zero of the function f(x) = (x-1)(x-2)?

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