## 3.2 Finding Gradient of a Tangent Line

#### Finding Gradient of a Tangent Line

**Recall that the tangent line to f(x) at point P(a,\ f(a)) has gradient f^{\prime}(a). Using these rules, we can find gradient of tangents of polynomial functions easily and quickly.**

Example

**Find the gradient of tangent line to the curve f(x)=3x^3-6x^2+1 at point (1,\ -2).**

f^{\prime}(x)=9x^2-12x, so the gradient when x=1 is f^{\prime}(1)=9 \times 1^{2}-12 \times 1=-3

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