Question

Find the slope of the tangent to the curve , x ≠ 2 at x = 10.

Answer 1

The given curve y is defined as,

y= x−1 x−2

The slope of the tangent for a curve y at a given point x= x 0 is given by,

slope= ( dy dx ) x= x 0

Substitute x−1 x−2 for y and 10 for x 0 .

( dy dx ) x=10 = ( ( x−2 )( 1 )−( x−1 )( 1 ) ( x−2 ) 2 ) x=10 = ( x−2−x+1 ( x−2 ) 2 ) x=10 = ( −1 ( x−2 ) 2 ) x=10 = −1 64

.