First Derivative Test

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

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

Tags

CCSS.HSA.REI.D.10

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.

When you check for sign changes at the critical points of a function, you are using the...

• Limit Test

• Intermediate Value Test

• 1st Derivative Test

• 2nd Derivative Test

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

• a maximum at x = -2.

• a minimum at

  x = -2 and a maximum at x = 4.

• a maximum at

  x = -2 and a minimum at x = 4.

• no maximum or minimum values.

True or False?

All critical points are extrema (maximums or minimums).

• True

• False

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSF.TF.A.4

True or False?

If the 1st derivative is positive on a certain interval, then that interval is decreasing.

• True

• False

If the first derivative of a function changes from positive to negative at a certain point, then that point is a known as a maximum.

• True

• False

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

• a maximum at x = -2.

• a maximum at x = 4.

• a maximum at x = -2 and a maximum and x = 4.

• no max or min values.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4