Question

Find the slope of tangent line at (1,-1.5)

Answer 1

Answer:

The slope of the tangent m = -0.0833

Step-by-step explanation:

Step(i):-

Given that the curve

      x y - 2y² + x² = -5 ...(i)

Differentiating equation (i) with respective to 'x', we get

  $x(\frac{dy}{dx} )+y (1) -2(2y)\frac{dy}{dx} + 2x=0$

    $x(\frac{dy}{dx} ) -2(2y)\frac{dy}{dx} = -2x-y$

    $(x -4y)\frac{dy}{dx} = -2x-y$

       $\frac{dy}{dx} = \frac{-2x-y}{x-4y}$

Step(ii):-

The slope of the tangent

$(\frac{dy}{dx})_{1,-1.5} = \frac{-2x-y}{x-4y}$

$(\frac{dy}{dx})_{1,-1.5} = \frac{-2(1)-(-1.5)}{1-4(-1.5)}$

       m =   $\frac{-2+1.5}{1+6}$

       $m = \frac{-0.5}{6} = -0.083$

The slope of the tangent m = -0.0833