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the curves y= 4x^2 + 2x -8 and y= x^3 -x +13 touch eachother at ......? (what is condition for two curves to touch eachother)

the curves y= 4x^2 + 2x -8 and y= x^3 -x +13 touch eachother at ......?

(what is condition for two curves to touch eachother)

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
The condition for the two curves to touch each other is that they should both have a common tangent at a particular (x,y) :
Hence, say they meet at (x1,y1). The slope of tangent at this point for both curves should be equal.
dy/dx = 8x1 + 2
dy/dx = 3(x1)^2 - 1
Hence, 3(x1)^2 - 1 = 8x1 + 2
Therefore, 3(x1)^2 - 8x1 - 3 =0

x1 = 3, -1/3
Now put x1 in both curves and find the value of y1. Only the value of y1 is same for both curves for x1 = 3 which is y1 = 34

Hence, they meet each other at (3, 34).

Thanks & Regards
Bharat Bajaj
askIITians Faculty
Qualification.
IIT Delhi

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