# Intermediate value theorem

• Jan 19th 2010, 05:04 PM
11rdc11
Intermediate value theorem
Ok so I know the idea why this is true but how would I prove it.

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

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
• Jan 19th 2010, 05:24 PM
Prove It
Quote:

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

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

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.
• Jan 19th 2010, 08:10 PM
Drexel28
Quote:

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

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

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

$\displaystyle f(0)=0,f(1001)=101^2+10\sin(1001)\geqslant 1000+10+10\sin(x)\geqslant1000$