curve sketching: Applying what you've learned
curve sketching is a fancy way to say "draw this graph." It might be easy for first and second degree or even third degree polynomials, but it is difficult to sketch a graph for some equations, and for that we use the first and second derivative tests to determine everything we need to know in order to draw the graph.
1. Use the first derivative test in order to determine intervals of increasing, decreasing, and relative extrema.
2. Use the second derivative test in order to determine intervals of concavity and points of inflection.
3. Use any other useful information given such as discontinuities and zeros.
4. Sketch the curve.
1. Use the first derivative test in order to determine intervals of increasing, decreasing, and relative extrema.
2. Use the second derivative test in order to determine intervals of concavity and points of inflection.
3. Use any other useful information given such as discontinuities and zeros.
4. Sketch the curve.
Problem 1 and solution:
Problem 2 and solution:
Problem 3 and solution: