First Derivative Test in Calculus

Given the Graph of f'(x), determine over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-5, 0) ∪ (2, ∞)

• (-5, ∞)

Given the graph of f(x), determine over what interval(s) is f(x) decreasing?

• (-3, 1)

• (-∞, -5) ∪ (0, 2)

• (-∞, -3) ∪ (1, ∞)

• (-5, 0) ∪ (2, ∞)

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

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

• True (Facts)

• False (Not Facts)

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

• True (Facts)

• False (Not Facts)

True or false: all critical points are extrema

• True

• False

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

• IVT

• MVT

• 1st Derivative Test

• 2nd Derivative Test

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.

Using the FIRST DERIVATIVE TEST....algebraically determine the intervals.

• A

• B

• C

• D