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the curve y=x 3 +x 2 -x has two horizontal tangents. the distance between these two tangents is

the curve y=x3+x2-x has two horizontal tangents. the distance between these two tangents is

Grade:12

2 Answers

Arun
25763 Points
one year ago

y' = 3x^2 + 2x - 1

 

3x^2 + 2x - 1 = 0

 

(3x - 1)(x + 1) = 0

 

x = 1/3, -1

 

at x = 1/3,

y = 1/27 + 1/9 - 1/3

y = -5/27

 

at x = -1,

y = (-1)^3 + (-1)^2 - (-1)

y = 1

 

the distance is 1 - (-5/27) = 32/27 units, C

Vikas TU
14149 Points
one year ago
Dear student 
dy/dx = 3x^2 + 2x -1 
from this x = -1, -1/3 
y(-1) = 1 
y(1/3) = -5/27 
y = -5/27
distance = |1+5/27|= 32/27 
 

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