Name
1325 WS 4.1, 4.2
Date
1. Find the intervals on which \(f(x)\) is increasing, the intervals on which \(f(x)\) is decreasing, and the local extrema.
Clearly identify all critical numbers, and show your work using a sign chart for \(f'(x)\).
a. \(f(x) = 5x^2 - 10x - 3\)
b. \(f(x) = \frac{9}{x} + x\)
2. Use the given information to sketch a graph of \(f(x)\). Assume \(f(x)\) is continuous on \((-\infty, \infty)\).
Identify any local extrema. Identify any points of inflection.
-3
0
1
2
4
5
f(x)
-4
0
2
1
-1
0
\(f'(x)\)
\(f''(x)\)
