javier123jmj javier123jmj
  • 11-03-2022
  • Mathematics
contestada

=
For the function f(x) = x2 – 6, find the equation of the tangent line at
X = -1.

Respuesta :

algebraic12 algebraic12
  • 11-03-2022

Answer:

[tex]y = - 2x - 7[/tex]

Step-by-step explanation:

One way is to differentiate the function

[tex] \frac{d}{dx} {x}^{2} - \frac{d}{dx} 6[/tex]

Use Power Rule

[tex]2x - 0[/tex]

[tex]2x[/tex]

P

[tex] - 2[/tex]

Plug in -1 so we get

That gives us the slope of the tangent line. we must find the point it passes through.

[tex]( - 1) {}^{2} - 6 = - 5[/tex]

So it have a slope of -2 and passes through (-1,-5)

So we use point slope form

[tex]y + 5 = - 2(x + 1)[/tex]

[tex]y = - 2x - 7[/tex]

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