Posted by **kelli** on Thursday, September 23, 2010 at 9:15pm.

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

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

- calculus -
**Reiny**, Thursday, September 23, 2010 at 10:15pm
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

## Answer This Question

## Related Questions

- calculus - prove that 5x - 7 - sin3x = 0 has at least one zero and prove that it...
- Math - Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to ...
- Trignometry - Can you please help me prove that ((1-cosx)/(1+cosx))=(cscx-cotx)^...
- Pre-calc - prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i ...
- Calculus - limit of (x*(y-1)^2*cosx)/(x^2+2(y-1)^2) as (x,y)->(0,1). By ...
- Precalculus/Trig - Prove the following identity: 1/tanx + tanx = 1/sinxcosx I ...
- Maths - Please help with these questions: (please show how to do) 1. How many ...
- Calculus - 1. Prove that (f(x+h)-f(x-h))/2=f'(x) 2. Prove that any parabola ...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- math - Let f:ℤ+ → ℤ+ be the function defined by: for each x &#...

More Related Questions