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\tf(x)\n-2\t0\n-1\t45\n0\t64\n1\t45\n2\t0\n3\t-35\n4\t0\n5\t189\n6\t640
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: Analyze the table
We check the $f(x)$ - values around each point. For $x = 0$, $f(-1)=45$, $f(0) = 64$, $f(1)=45$. Since $64>45$, $(0,64)$ is a local - maximum. For $x = 3$, $f(2)=0$, $f(3)=- 35$, $f(4)=0$, so $(3,-35)$ is a local minimum. For $x = 5$, $f(4)=0$, $f(5)=189$, $f(6)=640$, so $(5,189)$ is not a local maximum as $f(6)>f(5)$. For $x = 2$, $f(1)=45$, $f(2)=0$, $f(3)=-35$, so $(2,0)$ is not a local maximum as $f(1)>f(2)$.
Answer:
$(0,64)$