Blnd A.

asked • 05/05/23

identify the coordinates of any local and absolute extreme points and inflection points. Graph the function.

y = x5 - 5x4 = x4(x - 5)

Mark M.

Equation has two equal signs.
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05/05/23

Doug C.

Here is a Desmos graph for you to take a look at. It shows the 1st derivative test and the test for concavity. You can enable the 1st and/or 2nd derivative graphs by enabling the buttons to the left of the "show" rows. desmos.com/calculator/lc6tixkkya Take a look then post a comment on areas where you need clarification.
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05/05/23

Mark M.

Doug C.: Desmos is a tool to verify algebraic work/calculation. It cannot be used in an assessment. Student should leaner how to take first and second derivative and analyze.
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05/05/23

Paul M.

tutor
I disagree, Mark (although I am NOT a teacher). I think students need to learn to use graphs...I learned years ago before computers to sketch graphs by hand; graphing calculators make the job easier (and perhaps less thoughtful) but visualizing maxima, minima, points of inflection etc is very instructive. I see DESMOS as not essentially different from a graphing calculator. However, I DO agree that students also need to learn to analyze algebraically. As usual just my 2 cents!
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05/05/23

Josh F.

tutor
The 2nd equals sign equates an equivalent expression for the function rule, written in factored form. Use the standard (general form) and power rule to differentiate and set the derivative = 0. The resulting quartic equation yields two distinct solutions, both of which are zeroes at which y ' changes signs. Thus, both are local extrema. A sign chart for y ' will determine which is a min and which a max. Note that because the parent function, y, is an odd degree polynomial, it can't have any global extrema. A similar process for y " will allow you to calculate the location of the point of inflection.
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05/05/23

1 Expert Answer

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Doug C. answered • 05/06/23

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