Question

x | f(x)
-2 | 0
-1 | 45
0 | 64
1 | 45
2 | 0
3 | -35
4 | 0
5 | 189
6 | 640
according to the table, which ordered pair is a local maximum of the function, f(x)?
(0, 64)
(3, -35)
(5, 189)
(2, 0)

Explanation:

Step1: Define local maximum

A local maximum is a point where the function value is greater than nearby points.

Step2: Check point (0,64)

At x=0, f(x)=64. Nearby x=-1: f(-1)=45; x=1: f(1)=45. 64>45, so it's a local maximum.

Step3: Check other options

(3,-35): f(2)=0, f(4)=0, -35<0 (local min). (5,189): f(4)=0, f(6)=640, 189<640 (not max). (2,0): f(1)=45, f(3)=-35, 0<45 (not max). Final answer is (0,64).

Answer:

(0, 64)