AP Calculus Video Quiz

What is the condition for a function to have a relative minimum at a point?

• The second derivative is negative.

• The second derivative is positive.

• The first derivative changes from negative to positive.

• The first derivative changes from positive to negative.

How can you determine if a function is concave down on an interval?

• The first derivative is negative.

• The second derivative is positive.

• The first derivative is positive.

• The second derivative is negative.

What is the purpose of using L'Hôpital's Rule?

• To determine concavity.

• To find the derivative of a function.

• To solve integrals.

• To evaluate limits of indeterminate forms.

Which of the following is an indeterminate form?

• 0/0

• 1/0

• Infinity/0

• 0/1

What is the candidates test used for?

• To determine concavity.

• To evaluate limits.

• To find relative extrema.

• To find absolute extrema.

When evaluating the absolute minimum, why are endpoints considered?

• Endpoints can be potential absolute extrema.

• Endpoints are only considered for relative extrema.

• Endpoints are always the minimum.

• Endpoints are never the minimum.

What is the significance of the area under the curve of f'?

• It helps find the value of f at a point.

• It shows the relative extrema of f.

• It indicates the slope of f.

• It determines the concavity of f.

How is the area of a semicircle calculated?

• πr²

• 2πr

• πr²/2

• πr

What does a positive slope of f' indicate about f?

• f is concave up.

• f is concave down.

• f is decreasing.

• f is increasing.

Why might you not need to calculate the area under the curve from 2 to 8 when finding the absolute minimum?

• The area is always zero.

• The area is always negative.

• The area is irrelevant to the minimum.

• The area is positive and does not affect the minimum found at f(2).