Question

Find the equation of the tangent(s) to the following graphs at the points(s) whose $x$ or $y$- coordinates is given:
$y=x^2-2$, where $y=-2$

Answer 1

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

when $y=-2,-2=x^2-2\Rightarrow x^2=0\Rightarrow x=0$

$\Rightarrow \frac{dy}{dx}=0$

$\Rightarrow$ Tangent is passing through $(0,-2)$ and has slope $=0$

$\Rightarrow$ equation : $y+2=0\Rightarrow y=-2$