Question

2 of 4 (2 comp se the graph of y f(x) to answer the questions. Complete parts a and b. relat y f(x) 10 answ (-4,7) 8 (4,7) ○A (-3,5) 4(3,5) 3 8 0 10 -8 -6 4 2 2 4 6 8 10 at (T O C. The -10J and at x (Type D. There Click to select and enter your answer(s).

Answer 1

(a). f has a relative minimum at x if f(x) is minimum value attained by f in some open interval around x.

We can see clearly from the graph that x=-3,0,3 are points where f has relative minimum and relative minima are values of y at x=-3,0,3

Therefore relative minima are y=5,-6,5

Hence (C) is correct option i.e. there are three relative minima. The leftmost relative minimum value is 5 and it occurs at x=-3. The central relative minimum value is -6 and it occurs at x=0. The rightmost relative minimum value is 5 and it occurs at x=3.

(b). f has a relative maximum at x if f(x) is maximum value attained by f in some open interval around x.

We can see clearly from the graph that x=-2,2, -4,4 and x less -4 and x greater than 4 areare poi where f has relative maximum and relative maxima are values of y at these points.

Therefore relative maxima are y=6,7.

Hence A,B,C all are incorrect.