Find the relative extrema The given function is:\[ g(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-2)^2/2} \]This equation represents a Gaussian function, which is a type of continuous probability distribution. In this context, it appears to be a normal distribution with a mean of 2, due to the \((x-2)\) term in the exponent. The standard deviation is 1, as indicated by the form of the exponent and the normalization factor \(\frac{1}{\sqrt{2\pi}}\).Key characteristics:- **Mean (\(\mu\))**: 2- **Standard Deviation (\(\sigma\))**: 1This function is useful in statistics and probability theory to describe data that clusters around a mean.

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Answered: g(x) 1 27 e-(x-2)²/2

Math

Calculus

g(x) 1 27 e-(x-2)²/2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Find the relative extrema

The given function is:

\[ g(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-2)^2/2} \]

This equation represents a Gaussian function, which is a type of continuous probability distribution. In this context, it appears to be a normal distribution with a mean of 2, due to the \((x-2)\) term in the exponent. The standard deviation is 1, as indicated by the form of the exponent and the normalization factor \(\frac{1}{\sqrt{2\pi}}\).

Key characteristics:

- **Mean (\(\mu\))**: 2
- **Standard Deviation (\(\sigma\))**: 1

This function is useful in statistics and probability theory to describe data that clusters around a mean.

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