+0  
 
0
119
2
avatar

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

Guest May 1, 2018
 #1
avatar+88871 
+2

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

CPhill  May 1, 2018
 #2
avatar
+1

thank you!

Guest May 1, 2018

6 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.