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

Oh no! Our educators are currently working hard solving this question.

In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics.

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

(a) Derive the polynomial of degree five that satisfies both the Legendre equation$$ \left(1-x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+30 y=0 $$ and the normalization condition $y(1)=1$(b) $\diamond$ Sketch your solution from (a) and determine approximations to all zeros and local maxima and local minima on the interval (-1,1)

$$\begin{array}{l}y(x)=\frac{63}{8} x^{5}-\frac{35}{4} x^{3}+\frac{15}{8} x \\\text { Local Max: }(-.7651,42),(.2852, .347) \\\text { Local Min: }(-.2852,-.347),(.7651,-.42) \\\text { Zeros: }(-.5385)(.5385)\end{array}$$

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 2

Basic Ideas and Terminology

Differential Equations

Missouri State University

Campbell University

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:31

Graph the polynomial, and …

01:47

02:50

Use the given information …

02:57

Number of Local Extrema Gr…

01:15

04:53

(a) Find the polynomial $f…

07:31

00:58

Find a second-degree polyn…

01:35

Cubic with parameters Loca…

01:42

So in this Bush and I have a polynomial minus two Expert plus three x plus five. This will be a parabola on DA. By observing carefully, I can fact rise it also minus If I take common two X squared minus three x ah minus five so it can be fact Tried as minors off two X square plus two X minus five X minus five. So this will remind us off two weeks if I take common X plus one minus one minus five actually again X plus one. So that comes out. Toby X plus one with a negative sign. And the lex minus five. So clearly the roads are minus one and five by toe. So it will be a quadratic like this. X Texas, the Y axis minus one comma zero five by tokuma zero on DA. It will have one maximum. All right. So it has exactly one maximum at this point. So I hope it just here. Thank you.

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Graph the polynomial, and determine how many local maxima and minima it has.…

Use the given information to (a) sketch a possible graph of the polynomial f…

Number of Local Extrema Graph the polynomial, and determine how many local m…

(a) Find the polynomial $f(x)$ of lowest degree, with integer coefficients a…

Find a second-degree polynomial (of the form $a x^{2}+b x+c$ ) such that $f(…

Cubic with parameters Locate all local maxima and minima of $f(x)=x^{3}-3 b …