# Two Segment Graph : Equation of Tangent and Calculation of Points

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Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!!

The graph of F consists of a semicircle and two line segments as shown (please see the attachment). Let g be the function given by:

g(x)= def.integral from 0 to x f(t)dt.

a Find g(3).

b Find all value of x on the open interval (-2,5) at which g has a relative maximum. Justify.

c Write an equation for the line tangent to the graph of g at x=3.

d Find the x coordinate of each point of inflection of the graph g on the open interval (-2,5). Justify.

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##### Solution Summary

A two segment graph is analyzed to find the equation of a tangent line and to calculate point values.

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Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!!

The graph of F consists of a semicircle and two line segments as shown (see attachment). Let g be the function given by:

a ...

###### Education

- 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."
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