Find equation of the tangent line to the curve the y=x^(4) at the point x_(0)=-1​

1 thought on “Find equation of the tangent line to the curve the y=x^(4) at the point x_(0)=-1​”

1. Answer:

   [tex]4x + y + 3 = 0[/tex]

   Step-by-step explanation:

   [tex]y = {x}^{4} [/tex]

   Slope of this graph will be given by:

   [tex] \dfrac{dy}{dx} = \dfrac{d {x}^{4} }{dx} = 4 {x}^{3} [/tex]

   Now slope when x = -1 will be -4

   Using that equation we have the y coordinate when x coordinate is -1 will be:

   [tex]y = { (- 1)}^{4} = 1[/tex]

   Now the equation of tangent:

   [tex] \dfrac{y – 1}{x + 1} = – 4 \\ \implies y – 1 = – 4x – 4 \\ \implies 4x + y + 3 = 0[/tex]

   Reply