MCV4U Unit 3 Curve Sketching

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 an inflection point at x = 3

• There is a local min at x = 3

• There is an x-intercept at x = 3

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 an inflection point at x = 3

• There is a local min at x = 3

• There is an x-intercept at x = 3

A _____ __ __________ can be found by setting f"(x) = 0, making a sign chart, and finding the point values between concave up and down intervals.

The concavity of a function is described by its ______ derivative

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

• increasing

• concave up

• concave down

• decreasing

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• concave up

• increasing

• decreasing

• concave down

The ________ numbers can be found by setting f'(x) = 0 and solving for x.

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point

• The concavity of the function is up at that point

• The concavity of the function is down at that point

• The function is decreasing at that point

List all of the x-locations of the points of inflection of the function whose derivative is graphed.

• {-4, -2, 0}

• {-2, 0, 1}

• {-2, 0}

• Cannot be determined

In the diagram given, which points lie on the curve f(x) where f'(x) < 0?

• A, C, E, G  

• B, F

• B, D, F  

• C, E