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Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$

 
 Feb 2, 2025
 #1
avatar+130313 
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The line has a slope = 5

 

The slope at any point on the parabola =  -12x

 

Set these = 

 

-12x = 5

 

x  = -5/12

 

So y= -6(-5/12)^2 =  -25/24

 

So

 

-25/24  = 5 (-5/12) + c

 

25/12 - 25/24 = c

 

50/24 - 25/24  =   c = 25/24

 

 

 

 

 

cool cool cool

 Feb 3, 2025

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