Explore BrainMass

# Real Analysis : Points on a Differentiable Function

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Let h be a differentiable function defined on the interval [0,3], and assume that h(0)=1 h(1)=2 and h(3)=2.
a- argue that there exists a point d belong to [0,3] where h(d)=d.
b-argue that at some point c we have h'(c)=1/3.
c-argue that h'(x)=1/4 at some point in the domain.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:07 pm ad1c9bdddf
https://brainmass.com/math/real-analysis/real-analysis-points-differentiable-function-30039

#### Solution Preview

Proof:
a. Let f(x)=h(x)-x. Then we have f(0)=h(0)-0=1-0=1>0, f(3)=h(3)-3=2-3=-1<0. According to the Intermeidate Value Theorem, we can find some d in [0,3], such that f(d)=0. This implies h(d)-d=0, so ...

#### Solution Summary

Points on a differentiable function are investigated in the solution.

\$2.49