1st & 2nd Derivatives

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

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

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

• 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

• (-3, 45)

• (0,-1)

• (2, 0)

• (2, -5)

• x=0

• x=-5

• x=2

• x=-3

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

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

• increasing
• decreasing
• concave up
• concave down

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)