Question

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

Answer 1

This is not a complete answer, but you can say that you see easily that this function is continuous and then you choose an arbitrary x, like x = 0 and calculate the value of f(x) which in this case is 0. then you choose an x like 1000 and calculate the value of this which is approximately 1 million. And because it is a continuous function it has to have a value c that satisfy that f(c) = 1000. There is a theorem about this, but I've forgotten it's name.

Answer 2

so its not a simple answer like c=???

Answer 3

Well, you probably can :) but I don't see how.

Answer 4

f(c)=c^2+10sinc=1000
=>c=31.5

Answer 5

The problem with your question is that you have a sin and x by itself, so you can't really get the x to be by itself. Here is a link to wolfram alpha with the solution, but I think your professor/teacher will be more proud if you use the other way because then you proove that a c exists that fullfills the criteria http://www.wolframalpha.com/input/?i=1000+%3D+x^2%2B10sin(x)&asynchronous=false&equal=Submit