according to the table, which ordered pair is a local maximum of the function, f(x)?\n(0, 64)\n(3, -35)\n(5…

according to the table, which ordered pair is a local maximum of the function, f(x)?\n(0, 64)\n(3, -35)\n(5, 189)\n(2, 0)\n\nx | f(x)\n-2 | 0\n-1 | 45\n0 | 64\n1 | 45\n2 | 0\n3 | -35\n4 | 0\n5 | 189\n6 | 640

according to the table, which ordered pair is a local maximum of the function, f(x)?\n(0, 64)\n(3, -35)\n(5, 189)\n(2, 0)\n\nx | f(x)\n-2 | 0\n-1 | 45\n0 | 64\n1 | 45\n2 | 0\n3 | -35\n4 | 0\n5 | 189\n6 | 640

Answer

Explanation:

Step1: Understand local maximum

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

Step2: Check each option from table

From the table, when (x = 0), (f(x)=64). The values of (f(x)) for (x=- 1) is (45) and for (x = 1) is (45). Since (64>45), ((0,64)) is a local - maximum. For ((3,-35)), the value before (x = 3) ((x = 2,f(2)=0)) and after ((x = 4,f(4)=0)) are both greater than (-35), so it's not a local maximum. For ((5,189)), (f(4) = 0) and (f(6)=640), and (640>189), so it's not a local maximum. For ((2,0)), (f(1)=45) and (f(3)=-35), and (45>0), so it's not a local maximum.

Answer:

((0,64))