Review of Chapter 4A

The 1st and 2nd Derivative Tests are similar in that they...

• Both determine if a critical point is a relative min, relative max, or neither.

• They are not similar at all.

• Both involve solving a system of equations.

• Both involve taking the limit of a function at a certain point.

TRUE or FALSE?

The 2nd Derivative Test is what we use to determine points of inflection and concavity.

• True

• False

If f '(8) = 0 and f "(8)=3, which of the following must always be TRUE?

• There is a local minimum at x = 8.

• f(8) = 3

• f(8) = 0

• There is a global minimum at x = 8.

If f is a twice differentiable function with f '(5) = 0 and f "(5) = -6, which of the following must be TRUE?

• x = 5 is a relative maximum

• x = 5 is a relative minimum

• f (5) > 0

• x = 5 is a point of inflection.

Match the following.

• the 2nd derivative to determine if a critical point is a local extrema and if so what type.

• Evaluating an integral means...

• the first derivative to determine if a critical point is a local extrema and if so what type.

• Critical points are...

• finding the slope of a tangent line.

• Finding a derivative means...

• finding the area under a curve.

• The 2nd Derivative Test uses...

• where the 1st derivative equals 0 or is undefined.

• The 1st Derivative Test uses...

The area of A = 5 and area of B = 8. What is the average value of f (x) on the interval [0, 7]?

• 3

• 13

• 1

The graph of f '(x) is given. If f (0) = -2, find f (3).

• 5

• 3

• 2

• 1

Consider the table of values for a differentiable function f over the interval [0, 8]. Calculate the LEFT Riemann Sum for the function over the interval [0, 8] using the four sub-intervals indicated in the table.

• 42

• 48

• 52

• 62