Q1. The normal distribution is a bell-shaped curve defined by: y=e^(〖-x〗^2 ) Use the golden-section search...

Q1. The normal distribution is a bell-shaped curve defined by: y=e^(〖-x〗^2 ) Use the golden-section search to determine the location of the inflection point of this curve for positive x.

PLEASE do the iterations on excel and show the written text in the cells. Thank you!

Expert Solution

An inflection point can be found by finding a minimum of the first derivative of a function. This point is where the first derivative, that is the slope, equals zero. So it is the point where the function changes from being positive to negative or vice versa. The golden section search method uses the fact that if we evaluate the function at two points relatively far apart, and then at two points in between these two, we can narrow our search range by determining which of the inner points is closest to the actual value where the derivative will be equal to 0. The search uses the principle that the golden ratio can help to determine the solution more quickly by determining good guesses for the two interior points.

Now, we take a look at the derivative graphically so as to try to determine a beginning interval. The graph of the function obtained using Desmos.com is:

Colby Messinger answered 22 hours ago

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solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0

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