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Calculus · Derivatives

Tangent line to x^2

x^{2}

Step by step

  1. f(x) = x^{2}

    Tangent line at x = 1: y = f(x₀) + f′(x₀)(x − x₀).

  2. f(1) = 1

    The point of tangency.

  3. f'(x) = 2 x,\quad f'(1) = 2

    The slope is the derivative there.

  4. y = 1 + 2(x - 1) = 2 x - 1

    Point-slope form, simplified.

Reveal the answer
y = 2 x - 1