48 / 178 C + + Microsoft Word - MTH_251_Jab_manual_cover.doc Problem 25.5 Answer

Question

48 / 178 C + + Microsoft Word - MTH_251_Jab_manual_cover.doc Problem 25.5 Answer the following question in reference to a continuous function g whose first derivative is shown in Figure 25.11. You do not need to state how you made your determination; just state the interval(s) or values of x that satisfy the stated property. Note: The correct answer to one or more of these questions may be "There is no way of knowing." 25.5.1 Over these intervals, g" is positive and increasing. 25.5.2 At these values of x , g is nondifferentiable. 25.5.3 Over these intervals, g is never negative. 25.5.4 At these values of x, every antiderivative of g is nondifferentiable. Figure 25.11 g' 25.5.5 Over these intervals, the value of g" is constant. + + 1) 25.5.6 Over these intervals, g is linear.

Explanation / Answer

1)
This is where g' is concave up
Happens over (-inf , -3)

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2)
This is possible only where g' is undefined
And thus it happens at x = 2 and x= 4

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3)
No way of knowing

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4)
No way of knowing

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5)
g'' is constant when g' is linear
So, (-3 , 2) U (2 , 4)

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6)
g is linear wherever g' is constant
So, (2 , 4)

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