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Finding the derivative of a function given graphically and finding local maxima and minima.

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For the function of f, given below in graph

(a) Sketch
(b) Where does change its sign
(c) Where does have local minima and maxima

Using the graph of write a brief description of complete sentences to describe the relationship between the following features of the function of:

(a) the local maxima and minima of
(b) the points at which the graph of changes concavity
(c) the sign changes of
(d) the local maxima and minima of

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The derivatives of graphed functions and local maxima and minima are found. The solution is detailed and well presented.

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For the function of , given below in graph

(a) Sketch
(b) Where does change its sign
(c) Where does have local minima and maxima

Using the graph of write a brief description of complete sentences to describe the relationship between the following features of the function of :
(a) the local maxima and minima of
(b) the points at which the graph of changes concavity
(c) the sign changes of
(d) the local ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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