The First Derivative Test (8.2.4)

Question 1

• Determining the sign of the derivative immediately to either side of a critical point reveals whether that point is a relative maximum, relative minimum, or neither.

Answer 1

• Determining the sign of the derivative immediately to either side of a critical point reveals whether that point is a relative maximum, relative minimum, or neither.

Question 2

• The first derivative test states that if c is a critical point of f, and f is continuous and differentiable on an open interval containing c (except possibly at c), then f(c) can be classified as follows:

1) If f (c) < 0 for x < c and f (c) > 0 for x > c, then f(c) is a relative minimum of f.
2) If f (c) > 0 for x < c and f (c) < 0 for x > c, then f(c) is a relative maximum of f

Answer 2

• The first derivative test states that if c is a critical point of f, and f is continuous and differentiable on an open interval containing c (except possibly at c), then f(c) can be classified as follows:

1) If f (c) < 0 for x < c and f (c) > 0 for x > c, then f(c) is a relative minimum of f.
2) If f (c) > 0 for x < c and f (c) < 0 for x > c, then f(c) is a relative maximum of f

Question 3

• On an interval, the sign of the first derivative of a function indicates whether that function is increasing or decreasing.

Answer 3

• On an interval, the sign of the first derivative of a function indicates whether that function is increasing or decreasing.