MATH100 December 2013
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 • Q10 (a) • Q10 (b) • Q11 •
Question 08 (a)
Full-Solution Problem. Justify your answer and show your work. Full simplification of numerical answers is required unless explicitly stated otherwise.
Let . Find the critical numbers of .
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is said to be a critical number/point of if the slope of the tangent line to at is 0, or if the slope does not exist.
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By the definition of a critical number, we must find the for which or for which does not exist:
Setting and applying the zero product property:
Note that is never equal to zero on the interval . However, is undefined at , so does not exist at .
Therefore the critical numbers of are .
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