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

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01:45

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd College

Lectures

04:40

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.

44:57

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.

03:09

Find a second-degree polyn…

04:28

Find a polynomial function…

01:43

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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