math quizes calc 1

Math 151 Quiz 9. Name: Due by the end of class on Thursday, December 1

Show all work neatly. Use proper notation throughout your solutions.

I. Use the First Derivative Test to find all local extrema (both coordinates) for f and the interval(s) on which f is increasing / decreasing.

𝑓 𝑥 = 6 𝑥 −

6 𝑥!

II. Use the Second Derivative Test to find all local extrema (both coordinates) of f.

𝑓 𝑥 = 𝑥! − 5 3 𝑥! + 1

[10 points]

[8 points]

III. Find the absolute maximum value and the absolute minimum value of f(x) = x3 - 3x2 - 24x + 2 on the interval [-1, 5].

[7 points]