Discussion Questions and Problems

Discussion Questions

M6-1 Explain how to find the slope of a straight line.
M6-2 Explain how to find the slope of a nonlinear function at a particular point, using limits.
M6-3 What is the procedure for finding the maximum or minimum of a function? How is the second derivative used in this process?
M6-4 What are critical points?

M6-5 Find the derivatives of the following functions.
1. $Y = 2 X^{3} - 3 X^{2} + 6$
2. $Y = 4 X^{5} + 2 X^{3} - 12 X + 1$
3. $Y = 1 / X^{2}$
4. $Y = 25 / X^{4}$
M6-6 Find the second derivative for each of the functions in Problem M6-5.
M6-7 Find the derivatives of the following functions.
1. $Y = X^{6} - 0.5 X^{2} - 16$
2. $Y = 5 X^{4} + 12 X^{2} + 10 X + 21$
3. $Y = 2 / X^{3}$
4. $Y = 25 / 2 X^{4}$
M6-8 Find the second derivative for each of the functions in Problem M6-7.
M6-9 Find the critical ...

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