What is the value of \(c\) if x * (3x + 1) < c if and only when \(x\in \left(-\frac{7}{3},2\right)\)?

Guest Jul 25, 2019

edited by
Guest
Jul 25, 2019

edited by Guest Jul 25, 2019

edited by Guest Jul 25, 2019

#1**+5 **

Let f(x) = x * (3x + 1) = 3x^{2} + 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

hectictar Jul 25, 2019

#1**+5 **

Best Answer

Let f(x) = x * (3x + 1) = 3x^{2} + 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

hectictar Jul 25, 2019