Calculas1?

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested.

y 6 + x 3 = y 2 + 9x, slope at (0, 1)

Captain Matticus, LandPiratesInc2020-06-17T17:38:42Z

y^6 + x^3 = y^2 + 9x
6y^5 * dy + 3x^2 * dx = 2y * dy + 9 * dx

x = 0 , y = 1

6 * dy + 0 * dx = 2 * dy + 9 * dx
4 * dy = 9 * dx
dy/dx = 9/4

Tangent slope: 9/4
Normal slope:  -4/9

y - 1 = m * (x - 0)
y - 1 = mx
y = mx + 1

Tangent line:  y = (9/4) * x + 1
Normal line:  y = (-4/9) * x + 1