Graphs of Polynomial Functions (8.4.1)

Question 1

• To graph a function:

1. Find critical points using the first derivative.
2. Determine where the function is increasing or decreasing.
3. Find inflection points using the second derivative.
4. Determine where the function is concave up or concave down.

Answer 1

• To graph a function:

1. Find critical points using the first derivative.
2. Determine where the function is increasing or decreasing.
3. Find inflection points using the second derivative.
4. Determine where the function is concave up or concave down.

Question 2

• On an interval, the sign of the first derivative indicates whether the function is increasing or decreasing. The sign of the second derivative indicates whether the function is concave up or concave down.

Answer 2

• On an interval, the sign of the first derivative indicates whether the function is increasing or decreasing. The sign of the second derivative indicates whether the function is concave up or concave down.