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

 Jul 25, 2019
edited by Guest  Jul 25, 2019
edited by Guest  Jul 25, 2019

Best Answer 

 #1
avatar+8853 
+5

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

 Jul 25, 2019
 #1
avatar+8853 
+5
Best Answer

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

hectictar Jul 25, 2019

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