Question

find the slope of tangent to the curve
y= x-1/x-2 ≠2 at x= 10​

Answer 1

given : y = (x - 1)/(x - 2)

to find slope at x = 10

let us find the derivative which itself is the slope

dy/dx = [( x- 2) * (1) - (x - 1) * 1]/(x - 2)² [ quotient law ]

=> dy/dx = (x - 2 - x + 1)/(x - 2)²

=> dy/dx = - 1/(x - 2)²_________1

now put x = 10 in equation 1

=> dy/dx = -1/(10 - 2)²

=> dy/dx = -1/64

therefore the slope of the tanget m = -1/64 at x = 10