Thread: show that there is a number c such that f(c) = 1000

Question: If f(x) = x^2 + 10 sinx, show that there is a number c such that f(c) = 1000.

I'm not too sure I understand the question but I plugged in 1000 as the y value in that rule and don't really no how to solve for x.

Any help would be greatly appreciated!
Thanks in advance!

Originally Posted by s3a

Question: If f(x) = x^2 + 10 sinx, show that there is a number c such that f(c) = 1000.

I'm not too sure I understand the question but I plugged in 1000 as the y value in that rule and don't really no how to solve for x.

Any help would be greatly appreciated!
Thanks in advance!

what does the Intermediate Value Theorem tell you?

That there is a point (c,N) in between (31, 957) and (32, 1030)?

Originally Posted by s3a

Question: If f(x) = x^2 + 10 sinx, show that there is a number c such that f(c) = 1000.

I'm not too sure I understand the question but I plugged in 1000 as the y value in that rule and don't really no how to solve for x.

Any help would be greatly appreciated!
Thanks in advance!

, , because of the continuity of and the intermediate value theorem, there exists such that for any fixed .
By the way, you dont need to solve the value to show its existence.
http://en.wikipedia.org/wiki/Intermediate_value_theorem