Question

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

Answer 1

HELLO DEAR,

we know the formula for finding the slope of tangent = $\bold{dy/dx}$at any point x

so, $\bold{frac{x - 1}{x - 2}}$ at x = 10.

now, using queatient rule

$\bold{dy/dx = \frac{1 * (x - 2) - 1 * (x - 1)}{(x - 2)^2}}$

$\bold{dy/dx = \frac{x - 2 - x + 1}{(x - 2)^2}}$

$\bold{dy/dx = \frac{-1}{(x - 2)^2}}$

so, dy/dx at point x = 10.

$\bold{dy/dx_{x = 10} = \frac{-1}{(10 - 2)^2}}$

$\bold{dy/dx_{x = 10} = \frac{-1}{64}}$

hence, slope of tangent = -1/64

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

hope this helps you ....