Question

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

Answer 1

this is a continuous function right? so you can pick a suitable number , say pi, and say that
\[f(\pi)<1000\] and then maybe 50 pi and say
\[f(50\pi)>1000\] and so it must be 1000 somewhere.
this was a very clumsy estimate, feel free to make a better one