Posted by **Desperate** on Wednesday, September 24, 2008 at 6:17pm.

The Image Theorem:

The image theorem, a corollary of the intermediate value theorem, expresses the property that if f is continuous on the interval [a, b], then the image (the set of y-values) of f on [a,b] is all real numbers between the minimum of f(x) on [a,b], inclusive. USE THE EXTREME VALUE THEOREM AS A LEMMA (A PRELIMINARY RESULT) TO PROVE THE IMAGE THEOREM.

## Answer this Question

## Related Questions

- calculus - Verify that the Intermediate Value theorem applies to the indicated ...
- Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...
- Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...
- calculus - Referring to the Mean Value Theorem and Rolle's Theorem, how can I ...
- Calculus - Verify the hypothesis of the mean value theorem for each function ...
- Calculus - Verify that the hypotheses of the Mean-Value Theorem are satisfied ...
- calculus - Verify that the hypotheses of the Mean-Value Theorem are satisfied on...
- Calculus - Given f(x) = -1/x, find all c in the interval [-3, -½] that satisfies...
- calculus - Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the ...
- Math - Use the Intermediate Value Theorem to show that there is a root of the ...

More Related Questions