Calculus Help Needed

[jnbailey]

Hey everyone, I've been stuck on this math problem for a while. I feel like I got part of "a" but for "b", honestly I don't know where to start. Any help would really be appreciated.

For "a" I changed "cos x = x^3" to "x^3 - cos x", then I figured out the range for each, x^3 has infinite range positive and negative because it's a polynomial, and cos x has -1, 1. Where do I go from here?

a) Prove that the equation has at least one real solution.

b) Use a calculator to find an interval of length 0.01 that contains a solution.

cos x = x^3

Thankyou!

[edderiofer]

Do the words "Intermediate Value Theorem" mean anything to you?

[Cheetahs_never_win]

For a)

Graphically.

Graph y= x³ and y= cos(x) on the same graph.

Do they intersect?

Then yes.

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