First Derivatives for Extrema

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

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

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

Which of the following could be the graph of f ' , the derivative of f ?

• 
• 
• 
• 
• 

• 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

• x=0

• x=-5

• x=2

• x=-3

• (-3, 45)

• (0,-1)

• (2, 0)

• (2, -5)

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 maximum.

• True (Facts)

• False (Not Facts)

Given a function f(x), if f'(x) < 0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing

• increasing

• concave up

• constant