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In this lesson, we will learn how to draw the curve of a function by finding its critical and inflection points and find the intervals where the function is decreasing and increasing.

Q1:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 + 1 ) ( 𝑥 − 2 ) 3 ?

Q2:

Given that the curve 𝑥 𝑦 + 𝑎 𝑥 + 𝑏 𝑦 = 0 2 has an inflection point at ( 3 , − 2 ) , what are the values of constants 𝑎 and 𝑏 ?

Q3:

Use the given graph of a function 𝑓 ′ ′ to find the 𝑥 -coordinates of the inflection points of 𝑓 .

Q4:

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

Q5:

Use the given graph of to find all possible intervals on which is increasing.

Q6:

Q7:

Use the given graph of to find all possible intervals on which is decreasing.

Q8:

Q9:

The graph of the first derivative 𝑓 ′ of a continuous function 𝑓 is shown. State the 𝑥 -coordinates of the inflection points of 𝑓 .

Q10:

Using the graph, determine the intervals of increase and decrease of the function.

Q11:

Q12:

Q13:

Consider the polynomial function whose graph is given below.

Use the given points and the fact that is a critical point of the function to determine .

Determine the intervals where .

Q14:

The graph of the derivative 𝑓 ′ of a function 𝑓 is shown. At what values of 𝑥 does 𝑓 have a local maximum or minimum?

Q15:

The graph of the first derivative 𝑓 ′ of a function 𝑓 is shown. What are the 𝑥 -coordinates of the inflection points of 𝑓 ?

Q16:

Using the graph, discuss the monotony of the function.