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In this lesson, we will learn how to find the intervals of decreasing and increasing of a function and the concavity of its graph using differentiation.

Q1:

The graph of the first derivative π β² of a continuous function π is shown. On what intervals is π increasing or decreasing?

Q2:

Determine the intervals on which the function is increasing and where it is decreasing.

Q3:

Which of the following statements is true for the function ?

Q4:

Q5:

Determine the intervals on which the function π ( π₯ ) = π₯ β 1 1 π₯ + 2 3 is concave up and down.

Q6:

The graph of a function π¦ = π ( π₯ ) is shown. At which point are d d π¦ π₯ and d d 2 2 π¦ π₯ both positive?

Q7:

The graph of a function π¦ = π ( π₯ ) is shown. At which point are d d π¦ π₯ and d d 2 2 π¦ π₯ both negative?

Q8:

Determine the intervals on which π ( π₯ ) = β π₯ + π₯ + 1 6 π₯ 3 2 is concave up and concave down.

Q9:

Let π ( π₯ ) = β 4 π₯ + 5 π₯ + 1 2 π₯ 3 2 . Determine the intervals where this function is increasing and where it is decreasing.

Q10:

Let π ( π₯ ) = β 2 π₯ + 3 π₯ + 1 2 π₯ 3 2 . Determine the intervals where this function is increasing and where it is decreasing.

Q11:

Q12:

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