Practice with the First Derivative Test

• No local extrema

Given this graph of f'(x), on what interval(s) is f increasing?

• [-1,2]
• [0,1] U [3,4]
• [-1,0] U [1,3]
• [2,4]

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

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

Use the sign chart for f'(x).  There is(are) ...

• a local maximum at x = -2.
• a local minimum at
  x = -2 and a local maximum at x = 4.
• a local maximum at
  x = -2 and a local minimum at x = 4.
• no extrema.

Tags

CCSS.HSA.APR.B.3

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Tags

CCSS.HSF.IF.B.4