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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 of a continuous function is shown. On what intervals is increasing or decreasing?

Q2:

Let . Determine the intervals where this function is increasing and where it is decreasing.

Q3:

Q4:

The graph of a function 𝑦 = 𝑓 ( 𝑥 ) is shown. At which point are d d 𝑦 𝑥 and d d 2 2 𝑦 𝑥 both positive?

Q5:

The graph of a function 𝑦 = 𝑓 ( 𝑥 ) is shown. At which point are d d 𝑦 𝑥 and d d 2 2 𝑦 𝑥 both negative?

Q6:

Determine the intervals on which the function 𝑓 ( 𝑥 ) = − 𝑥 − 8 𝑥 2 is increasing and where it is decreasing.

Q7:

Determine the intervals on which is concave up and concave down.

Q8:

Determine the intervals on which the function is concave up and down.

Q9:

Which of the following statements is true for the function 𝑦 = 4 − 6 𝑥 + 3 𝑥 2 ?

Q10:

Which of the following statements is true for the function ℎ ( 𝑥 ) = − 𝑥 − 2 𝑥 + 1 2 ?

Q11:

Which of the following statements is true for the function 𝑔 ( 𝑥 ) = − 𝑥 − 1 4 𝑥 − 4 7 2 ?

Q12:

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