Which interval for the graphed function contains the local maximum? a ( -3,-2) b (-2,0) c (0,2) d (2,4)

Option C is correct .i.e., ( 0 , 2 )

Step-by-step explanation:

We are given with a graph.

To find: Interval of local maximum

We can clearly see from graph that there is only one point of maximum.

Point of maximum is ( 1.55 , 10.8 )

Option A:

Interval is ( -3 , -2 ) means x > -3 & x < -2

but this interval does not contain x-coordinate of point of Maximum.

Thus, this option is incorrect

Option B:

Interval is ( -2 , 0 ) means x > -2 & x < 0

but this interval does not contain x-coordinate of point of Maximum.

Thus, this option is incorrect

Option C:

Interval is ( 0 , 2 ) means x > 0 & x < 2

Here, this interval contain x-coordinate of point of Maximum.

Thus, this option is correct

Option D:

Interval is ( 2 , 4 ) means x > 2 & x < 4

but this interval does not contain x-coordinate of point of Maximum.

Thus, this option is incorrect

Therefore, Option C is correct.

m∠a is 90°

m∠b is 40°