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In this lesson, we will learn how to find local extrema using the second derivative test.

Q1:

Find, if any, the points ( π₯ , π¦ ) where π¦ = π₯ + 3 π₯ β 1 6 3 2 has a local maximum or local minimum.

Q2:

Find, if any, the point ( π₯ , π¦ ) where π¦ = β π₯ + 4 π₯ β 6 2 has a local maximum or local minimum.

Q3:

Find the local maxima/minima of the function π ( π₯ ) = 3 π₯ β 2 π₯ 4 3 .

Q4:

Use the second derivative test to find, if possible, the local maximum and minimum values of π ( π₯ ) = 9 π₯ β 2 π₯ β 5 4 2 .

Q5:

Determine the local maximum and minimum values of the function π¦ = β 3 π₯ β 6 π₯ β 4 2 .

Q6:

Determine the local maximum and local minimum values of π ( π₯ ) = 4 π₯ β 1 2 π₯ β 5 3 .

Q7:

Find where (if at all) the function π ( π₯ ) = β 2 π₯ β 9 π₯ β 1 2 π₯ β 1 5 3 2 has its local maxima and minima.

Q8:

Find the local maximum and minimum values of the curve that passes through the point ( β 1 , 7 ) where the gradient of the tangent is 6 οΉ π₯ + 4 π₯ + 3 ο 2 .

Q9:

Find the points ( π₯ , π¦ ) where π¦ = 9 π₯ + 9 π₯ has a local maximum or a local minimum.

Q10:

Find, if any, the local maximum and local minimum values of π ( π₯ ) = 1 9 π₯ + 1 5 π₯ s i n c o s , together with their type.

Q11:

Find, if any, the local maximum and local minimum values of π¦ = 7 π₯ + 7 π₯ .

Q12:

Find the local maxima and local minima of π ( π₯ ) = β 5 π₯ 3 + 2 π₯ β 1 6 π₯ 2 l n , if any.

Q13:

Find the local maximum and minimum values of π ( π₯ ) = 2 β π₯ β 4 β π₯ 4 .

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