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Calculus · Derivatives

Tangent line to sqrt(25 - x^2)

\sqrt{25 - x^{2}}

Step by step

  1. f(x) = \sqrt{25 - x^{2}}

    Tangent line at x = 3: y = f(x₀) + f′(x₀)(x − x₀).

  2. f(3) = 4

    The point of tangency.

  3. f'(x) = - \frac{x}{\sqrt{25 - x^{2}}},\quad f'(3) = - \frac{3}{4}

    The slope is the derivative there.

  4. y = 4 + - \frac{3}{4}(x - 3) = \frac{25}{4} - \frac{3 x}{4}

    Point-slope form, simplified.

Reveal the answer
y = \frac{25}{4} - \frac{3 x}{4}