Let's find the derivative of y:
[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]Evaluate the derivative for x = 2:
[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]Now, we have the slope, let's use the point-slope formula to find the equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]Answer:
y = 8x - 21
