AP Calculus Justification

To justify that a function is continuous you must show... 

• f(c) is defined

• All of these

What must you do to show that a limit exists?

• All of these

When does a curve have a horizontal tangent line?

• When x = 0

• When y = 0

When does a curve have a vertical tangent line

• When x = 0

• When y = 0

What is the justification for absolute extrema?

• Candidates Test

• First Derivative Test

• Second Derivative Test

• Intermediate Value Theorem

What is the justification for a function to be decreasing?

• Function is increasing

• First Derivative is Positive

• First Derivative is Negative

• Second Derivative is Positive

Given the graph of the derivative of a function, how can you tell if the function is concave up.

• The graph is positive

• The graph changes from positive to negative

• The graph changes from negative to positive

• The graph is increasing

What must be true for an x-value to be a critical number?

• A) The x-value is in the domain of the function

• B) The derivative at the x-value is 0 or undefined

• C) The derivative at the x-value is equal to the average value

• D) Both A and B

What is the justification for a function having a local minimum?

• The derivative changes from positive to negative

• The derivative changes from negative to positive

• The derivative changes from increasing to decreasing

• The derivative changes from decreasing to increasing?

For a point to be a local maximum according to the second derivative, f'(x)=0 and what else?

• The second derivative is negative

• The second derivative is positive

• The function crosses the x-axis

• The function crosses the y-axis