Question

Set up an equation of a tangent to the graph of the following function.
$y=-x^2-1$ at the points $x=2.$

Answer 1

$y=-x^2-1$

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

${\left(\frac{dy}{dx}\right)}_{x=2}=-4$

The co-ordinate of y for x=2 is

$y=-2^2-1=-5$

The equation of tangent is $(x-2)(-4)=y+5\Rightarrow 4x+y-3=0$