Application of Differentiation

What is the stationary point for the curve y=x² - 4?

• A minimum at ( 0, -4)

• A maximum at (0, -4)

• A minimum at (0,4)

• A maximum at (0,4)

What is the stationary points for the curve f(x) = x³ +3x² - 24x and determine their nature.

• Maximum point : (2, -28) and minimum point : (-4, 80)

• Minimum point : (2, 28) and maximum point : (-4, 80)

• Minimum point : (2, -28) and maximum point : (4, 80)

• Minimum point : (2, -28) and maximum point : (-4, 80)

Extremum points are either

• local maximum

• fixed point

• inflection point

• local minimum

Local maximum point is obtained when

• f ' (x) exchange from negative to positive

• f '' (x) exchange from positive to negative

• f ' (x) exchange from positive to negative

• f '' (x) exchange from negative to positive

Local minimum point is obtained when

• f ' (x) exchange from negative to positive

• f '' (x) exchange from positive to negative

• f ' (x) exchange from positive to negative

• f '' (x) exchange from negative to positive

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

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSS.ID.C.7

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined