Prove that there is a number that is exactly one more than its cube. (don’t solve just show there is one)

Question

Prove that the function f(x)= cosx-x has a zero in (o. pi/2) Justify.

Answer 1

x = x^3 + 1
x^3 - x + 1 = 0

let f(x) = x^3 - x + 1

every cubic function, just like every odd exponent equation, crosses the x-axis at least once.

BTW, how about x = appr. -1.3247

for cosx - x = 0
cosx = x

graph y = cosx an y = x on the same graph
they only cross once, hence one solution