# Worksheet: First Derivative Test for Finding Local Extrema

Q1:

Find the point where has a critical point, and determine whether it is a local maximum or local minimum.

• A , local minimum
• B , local maximum
• C , local maximum
• D , local minimum
• E , local minimum

Q2:

Locate and classify the critical points of .

• Alocal maximum at , local minimum at
• Blocal maximum at , local minimum at
• Clocal maximum at , local minimum at
• Dlocal maximum at , local minimum at
• Elocal maximum at , local minimum at

Q3:

Find the local maximum and minimum values of .

• AA local maximum value is at .
• BA local minimum value is at .
• CA local minimum value is at .
• DA local maximum value is at .
• EA local maximum value is at .

Q4:

Find the local maximum and local minimum values of . Give your answers to the nearest integer.

• AThe local minimum is 0, and the local maximum is 4.
• BThe local maximum is 0, and the local minimum is .
• CThe local maximum is 0, and the local minimum is 7.
• DThe local minimum is 0, and the local maximum is 3.

Q5:

Find (if any) the local maxima and local minima of .

• A local maximum at .
• B local minimum at .
• C local minimum at .
• D local maximum at .
• E local maximum at .

Q6:

Determine where the local maxima and minima are for .

• Alocal maxima at , local minima at and
• Blocal maxima at and , local minima at
• Clocal maxima at , local minima at and
• Dlocal maxima at , local minima at and

Q7:

Find, if any, the local maximum and local minimum values of .

• AThe local minimum is.
• BThe local minimum is.
• CThe local maximum is.
• DThe local maximum is.

Q8:

Identify and classify the critical points of as local maxima, local minima, or neither.

• AThere are no critical points.
• Blocal minimum at
• CThe critical point at is neither a local maximum nor local minimum.
• Dlocal maximum at
• EThis cannot be determined.

Q9:

Find, if any, the local maximum and local minimum values of .

• Ahas no local maximum or minimum points
• Blocal minimum value:
• Clocal maximum value:
• Dlocal maximum value:
• Elocal minimum value:

Q10:

Let , find where the local maxima and local minima occur for .

• Alocal maximum at , local minimum at
• Blocal maximum at , local minimum at
• Clocal maximum at , local minimum at
• Dlocal maximum at , local minimum at
• Elocal maximum at , local minimum at

Q11:

Find the point where has a critical point, and determine whether it is a local maximum or local minimum.

• A , local minimum
• B , local minimum
• C , local maximum
• D , local maximum

Q12:

Find the local maximum and minimum values of .

• Alocal maximum at
• Blocal maximum at
• Clocal minimum at
• Dlocal minimum at
• EThe function has no local maxima or minima.

Q13:

Find the critical point of that satisfies , and then state whether is a local maximum or a local minimum.

• A , local minimum
• B , local maximum
• C , local maximum
• D , local minimum