Question

Let f(x) = x^3+x-sin(x) prove that there exists p belongs to real number such that f(p) = 0.

Answer 1

f(x) = x³ + x - sinx
differentiator with respect to x
df(x)/dx = 3x² + 1 - cosx

df(x)/dx = 0 at x = 0

hence, x = 0 is the point where f(x) = 0