- #1

Arnoldjavs3

- 191

- 3

## Homework Statement

http://prntscr.com/daze68

What I don't understand:

**1. "P be a polynomial with degree n"**

do these equations satisfy this description?:

$$p(x) = (x^2 + x)^n$$

$$p(x) = (5x^2 + 2x)^n$$

etc.

**2. "C1 is a curve defined by y=p(x)"**

c1 is essentially just the curve of the polynomial?

**3. p(x) = e^x**

This is meant to find points of intersection(which are also called roots? Correct me if I'm wrong) right? That there are n solutions to this?

**4. h(x) = p(x) - e^x**

Where does this h(x) function come from? I thought this would equal to 0 if you rearrange the equation from

3. Is it just a function introduced for the sake of answering this problem?

**5. "Since p is of degree n, the nth derivative is just a constant"**

What is this saying? That after differentiation n is still a constant? Since it's a polynomial it has to be some constant to begin wtih right?

**6. How do they go from h(x) = p(x) - e^x to h^(n)(x) = 0 and why does it have only one solution/root?**

If you differentiate then it becomes h'(x) = p'(x) - e^x right?

I know that the MVT states( i think ) that the derivative will have n-1 roots. There exists a root between the interval of its original function but how does that apply here? Sorry if this is inappropiate for a question i just don't understand the problem at its core.