Analyzing Functions with Derivatives

If a function has a second derivative that is positive, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

If a function has a second derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

If a function has a derivative that is positive, what does that tell you?

• The function is increasing
• The function is decreasing

Tags

CCSS.HSF.IF.B.4

Where does the function, f(x) = 2x³ - 9x² - 12x -3 have relative max/min values?

• Rel max x = -1, Rel min x = 2

• Rel min x = 1, Rel min x = 2

• Rel max x = 1, Rel min x = 2

• Rel max x = 2, Rel min x = 1

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

• (-∞, 0]

• (-1, 0]

• (0, ∛2]

• (∛2, ∞)

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

Tags

CCSS.HSF.IF.B.4

Over what interval(s) is f(x) decreasing?

• (-3, 1)
• (-∞, -5) ∪ (0, 2)
• (-∞, -3) ∪ (1, ∞)
• (-5, 0) ∪ (2, ∞)

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

• -2
• 0
• 2
• None

The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given by v(t) = t³ - 3t² + 12t + 4 is

• 9
• 12
• 14
• 21