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 neighboring points.

Step2: Check each point

For $x = - 2$, $f(-2)=0$, $f(-1) = 45>0$. For $x=-1$, $f(-1) = 45$, $f(0)=64 > 45$. For $x = 0$, $f(0)=64$, $f(1)=45<64$, $f(-1)=45<64$. For $x = 1$, $f(1)=45$, $f(2)=0<45$, but $f(0)=64>45$. For $x = 2$, $f(2)=0$, $f(3)=- 35<0$, but $f(1)=45>0$. For $x = 3$, $f(3)=-35$, $f(4)=0>-35$. For $x = 4$, $f(4)=0$, $f(5)=189>0$. For $x = 5$, $f(5)=189$, $f(6)=640>189$.

Answer:

$(0,64)$