Question

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

Answer 1

5jgernncjxjdndhxjsjhsbdhchhx

Answer 2

Find the slope of the tangent to the curve,y = (x - 1)/(x - 2), x ≠ 2 at x = 10.

solution :- we know, slope of tangent of curve = value of 1st derivative of given curve.

$y=\frac{x-1}{x-2}\\\\\text{differentiate y with respect to x }\\\\\frac{dy}{dx}=\frac{(x-2)\frac{d(x-1)}{dx}-(x-1)\frac{d(x-2)}{dx}}{(x-2)^2}\\\\\frac{dy}{dx}|_{x=10}=\frac{x-2-(x-1)}{(x-2)^2}\\\\\frac{dy}{dx}_{x=10}=\frac{-1}{(10-2)^2}=\frac{-1}{64}$

hence, slope of tangent = -1/64