What is the value of c if x * (3x + 1) < c if and only when x∈(−73,2)?
+9488 Let f(x) = x * (3x + 1) = 3x2 + x
Let's see what f(x) is when x is at the endpoints of the interval.
f(-7/3) = 3(-7/3)2 + (-7/3) = 14
f(2) = 3(2)2 + 2 = 14
Aha! they are the same, just as I suspected! 🕵️♀️
Let's see what f(x) is when x is in the interval.
f(0) = 3(0)2 + 0 = 0
And it is true that 0 < 14
Since f(x) is a parabola, we can be sure that f(x) < 14 if and only if x is in the interval (-7/3, 2)
Here's a graph: https://www.desmos.com/calculator/bcaogdbdtx
+9488 Let f(x) = x * (3x + 1) = 3x2 + x
Let's see what f(x) is when x is at the endpoints of the interval.
f(-7/3) = 3(-7/3)2 + (-7/3) = 14
f(2) = 3(2)2 + 2 = 14
Aha! they are the same, just as I suspected! 🕵️♀️
Let's see what f(x) is when x is in the interval.
f(0) = 3(0)2 + 0 = 0
And it is true that 0 < 14
Since f(x) is a parabola, we can be sure that f(x) < 14 if and only if x is in the interval (-7/3, 2)
Here's a graph: https://www.desmos.com/calculator/bcaogdbdtx
