💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# A number $a$ is called a fixed point of a function $f$ if $f(a) = a$. Prove that if $f'(x) \not= 1$ for all real numbers $x$, then $f$ has at most one fixed point.

## Fixed point couldn't exist more than 1

Derivatives

Differentiation

Volume

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

so we're showing that F of X is equal to acts. That's only one solution is, uh, derivative of X is not equal to one. We have the function G of acts. We're gonna make it equal to F X minus. That's then we have the derivative of G of X is equal to the derivative of EPA VAX minus one is not equal to zero. Then we're gonna apply rules. Zero. You see that G FX has only 10 so f of X equals acts passed only one solution.

Derivatives

Differentiation

Volume

Lectures

Join Bootcamp