Concavity and Function Behavior, Increasing and Decreasing, Derivative Tests

What are the asymptotes?

• x=1, x= 2, y =1, y= 2
• x= 2, x=-2, y = 1
• x=2 y =-1
• x=1 y =2, y =-2

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

• decreasing
• increasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

• increasing

• decreasing

• convex

• concave

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3

• There is a local min at x = 3

• There is an inflection point at x = 3

• There is an x-intercept at x = 3

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

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