Function Analysis - Concept Review

If f'(c) changes from (-) to (+) then which of the following must be true?

• f has a relative max at x = c

• f has a relative min at x = c

• f has a non-extreme horizontal tangent at x = c

• None of these must be true

If f'(x) > 0 then f(x) must be...

• Increasing

• Positive

• Decreasing

• Negative

If f' is decreasing through the x-axis at x = c, then which of the following must be true?

• f has a relative max at x = c

• f has a relative min at x = c

• f has a non-extreme horizontal tangent at x = c

• None of these must be true

If f''(x) < 0 then f(x) must be...

• Increasing

• Concave Up

• Decreasing

• Concave Down

If f''(x) < 0 then f'(x) must be...

• Increasing

• Concave Up

• Decreasing

• Concave Down

If f''(x) > 0, then f(x) must be...

• Concave up

• Increasing

• Concave Down

• Decreasing

If f'(c) = 0 then which of the following must be true?

• f has a relative max at x = c

• f has a relative min at x = c

• f has a horizontal tangent at x = c

• None of these must be true

A line connects the points (3, 1) and (8, -3). At what value of x does the line cross the x-axis?

• 4.25

• 1.75

• 4.75

• 5.25

Where do points of inflection occur on the graph of the derivative function?

• When f'(x) crosses the x-axis

• When f'(x) has a max/min

• When f'(x) changes signs

• When f'(x) has a horizontal tangent

What values of x are chosen to create the sign chart of f'(x)?

• the values of x such that f'(x) has a max or a min

• the values of x such that f'(x) has a minimum

• the values of x such that f'(x) has a maximum

• the values of x such that f'(x) = 0