Connecting f, f', and f'' Graphically

Let f(x) be pictured.

Identify the x-value(s) where f(x) has a point of inflection.

• x = 1.5

• x = 4

• x = 1

• x = 6

• x = 8

Let f(x) be pictured.

Identify the x-value(s) where f(x) is concave up.

• (1.5, 2.5)

• (3.5, 4.5)

• (6, 8)

• (0, 1)

• (4.5, 6)

Let f(x) be pictured.

Identify the x-value(s) where f(x) is concave down.

• (0, 1.5)

• (2.5, 3.5)

• (4.5, 6)

• (1.5, 2.5)

• (6, 8)

Let f(x) be pictured.

Identify the x-value(s) where f(x) has a relative max.

• x = 1

• x = 2

• x = 3

• x = 4

• x = 5

Let f(x) be pictured.

Identify the x-value(s) where f(x) has a relative min.

• x = 1

• x = 2

• x = 3

• x = 4

• x = 7

Let f'(x) be pictured.

Identify the x-value(s) where f(x) has a relative max.

• x = 1

• x = 3

• x = 5

• x = 6

• x = 8

Let f'(x) be pictured.

Identify the x-value(s) where f(x) has a relative min.

• x = 2

• x = 4

• x = 7

• x = 6

• x = 8

Let f'(x) be pictured.

Identify the x-value(s) where f(x) has a critical value.

• x = 1

• x = 6

• x = 3

• x = 4

• x = 7

Let f'(x) be pictured.

Identify the x-value(s) where f(x) is concave up.

• (0, 1)

• (7, 8)

• (4, 5)

• (1.5, 2.5)

• (6, 8)

Let f'(x) be pictured.

Identify the x-value(s) where f(x) is concave down.

• (1, 2)

• (5, 7)

• (3, 4)

• (0, 1.5)

• (4, 6)