# Thread: Intermediate value theorem

1. ## Intermediate value theorem

Ok so I know the idea why this is true but how would I prove it.

If $f(x) = x^2 + 10\sin{x}$ show that therre is a number c such that $f(c) = 1000$

I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks

2. Originally Posted by 11rdc11
Ok so I know the idea why this is true but how would I prove it.

If $f(x) = x^2 + 10\sin{x}$ show that therre is a number c such that $f(c) = 1000$

I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks
If you can prove the statements you said - i.e. that the function is continuous and has an infinite range, then you will have proven your if statement.

3. Originally Posted by 11rdc11
Ok so I know the idea why this is true but how would I prove it.

If $f(x) = x^2 + 10\sin{x}$ show that therre is a number c such that $f(c) = 1000$

I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks
$f(0)=0,f(1001)=101^2+10\sin(1001)\geqslant 1000+10+10\sin(x)\geqslant1000$