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Find the linearization $ L(x) $ of the function at $ a. $$ f(x) = x^3 - x^2 + 3, a = -2 $
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Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 10
Linear Approximation and Differentials
Derivatives
Differentiation
Missouri State University
Campbell University
Baylor University
University of Nottingham
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.
03:25
Find the linearization $L(…
02:32
01:56
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02:34
Okay, We know L A box is half of a post up prime of eight times X minus a. They're for UVA is negative. Eight, that is, four plus three equals negative. Nine. A primal X is three x squared, minus two acts. They're for a problem. Negative to plugging that in three times. Four months, two times negative to a 16. Therefore, L A box is negative. Nine was 16 times exposed to. Therefore, this simplifies to 16 acts close 23.
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