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The equation $ y" + y' - 2y = x^2 $ is called a d…
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Problem 67 Hard Difficulty

Find a second-degree polynomial & P & such that $ P(2) = 5, P'(2) = 3, $ and $ P"(2) = 2. $

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Frank Lin

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Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

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Derivatives

Differentiation

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Top Calculus 1 / AB Educators
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Anna Marie Vagnozzi

Campbell University

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Oregon State University

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Calculus 1 / AB Courses

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04:40
Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
Video Thumbnail

44:57
Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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03:09

Find a second-degree polyn…

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Problem 1
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Problem 13
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Problem 16
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Problem 45
Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
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Problem 63
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Problem 65
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Problem 67
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Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

it's clear. So when you read here so we have a P of X is equal to a X square plus B x plus c. So our first derivative, it has to be to a X plus be in our second derivative. Must to be too, eh? We're gonna plug in to what's to pay Becomes a is equal to one. So our first derivative is equal to two x plus being the first orbit of to a sequel to two comes too close. Be just equal to three. He is equal to negative one. So P f X is equal to x square minus X plus c. You have PF two is equal to two square minus two plus C, which is equal to five. C is equal to three, so you get your backs is equal to X squared minus X plus three.

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Related Topics

Derivatives

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40
Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
Video Thumbnail

44:57
Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
Join Course
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