Question

Find the equation of the normal line to the curve f(x) = 2x^3 + 1 at the point (1, 3).

Answer 1

Answer:

x + 6y = 19

Step-by-step explanation:

slope of the tangent line = f'(x)

f(x) = 2x³ + 1

f'(x) = 6x²

f'(1) = 6(1)²

     = 6

slope of the normal line = (-1) ÷ slope of the tangent line

                                        = (-1) ÷ 6

                                        = -1/6

equation of the normal line:

$\boxed{y-y_1=m(x-x_1)}$

$y-3=-\frac{1}{6} (x-1)$

$6(y-3)=-x+1$

$x+6y=19$