Write the equation of the tangent line to the graph of y = x^3 at the point x = 1.

Question

The tangent line is _____ (Type an​ Equation).

Answer 1

The slope of the tangent line is the derivative of the function.

y' = 3x²

at x = 1, the slope of the tangent line is 3

The point on the curve, x³, where the slope is 3 is at (1, 1).

y -1 = 3(x-1)

y = 3x-3 +1 = 3x-2

The slope-intercept form of the tangent line is y = 3x-2