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The curves Y=ax^2 +b and Y=2x^2 +cx have a common tangent line at the point (-1,0). Find a,b and c. 

 

Thank you

 May 1, 2018
 #1
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y = ax^2 + b        y  = 2x^2 + cx

 

Since the point (-1, 0)   is on both graphs

 

Using the first function, we have

 

0 = a(-1)^2 + b

 

0  =  a  + b

 

Using the second function, we have that

 

0 = 2(-1)^2 + c(-1)

0 = 2  - c

c = 2

 

Taking the derivative of both functions

 

y'  = 2ax               y'  = 4x + c

 

y' = 2ax               y' =  4x + 2

 

The slope of the tangent line is the same for both functions at x  = -1

 

So....equating slopes

 

2a(-1)   =  4(-1) + 2

 

-2a  =    -4 + 2

 

-2a  = = -2

 

a  =  1

 

And since a + b  = 0

 

b  =  -1

 

The equation of the tangent line is

 

y =  (4(-1) + 2) ( x  - -1)

 

y =  -2(x + 1)

 

y =  -2x -2

 

Here's a graph  :  https://www.desmos.com/calculator/2wiesd0ekz

 

 

cool cool cool

 May 1, 2018
 #2
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+1

thank you!

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