First Derivative Test

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a

• decreasing

• increasing

• concave up

• constant

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3. #3

• increasing
• decreasing
• concave up
• concave down

What are inflection points in calculus? #13

• Inflection points are points where the curve intersects the x-axis

• Inflection points are points where the curve intersects the y-axis

• Inflection points are points where the curve is at its highest or lowest

• Inflection points in calculus are points on a curve where the concavity changes, indicating a change in the direction of the curve's curvature.

True or false: all critical points are extrema

• True

• False

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.

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

Which intervals of the graph are increasing?

f(x) = 2x⁴ - 4x² + 1

• (-1,0)

• (0,1)

• (-∞,-1) and (1,∞)

What is the maximum?

f(x) = x³ - 3x² - 1

• (0,-1)

• (-1,-5)

• (2,-5)

• (5,49)