Questions regarding a graph

Question

 

b and c are fine but confused with a, d and e

 

 

QUESTION TWO

 

Answer 1

(1).(a).

Find the x - coordinate of the critical points of f(x) :

From the graph, the x - coordinate of the critical points of f(x) are - 0.5, 0.5, 1.5 and 2.5 because f(x) has a relative maximum or relative minimum at these numbers.

The options second, fourth, sixth and eighth are correct .

 

(1).(d).

The nature of the curve at x = 0 :

From the graph, the curve gradually increasing(every x-value) from - 0.5 and reach the maximum point at x = 0.5. So, the nature of the curve at x = 0 is local maximum.

The first option is correct .

 

(1).(e).

The nature of the curve at x = 1 :

From the graph, the curve gradually decreasing(every x-value) from 0.5 and reach the minimum point at x = 1.5. So, the nature of the curve at x = 1 is local minimum.

The second option is correct .

 

Answer 2

(2).(a).

From the graph, the curve increasing from x = 0 to x = 3, so the the interval of concave down ward is (0, 3).

 

(2).(b).

Find the x - values of the inflection points :

From the graph, the x - values of the inflection points are - 1 and 2, because the concavity of f(x) changes from upward to downward (or downward to upward) at these x-values.

The second and fifth options are correct answer.