Calculus, 2ADV C1 EQ-Bank 18 Let \(f(x)=6 \sqrt{x+1}+5\). Find the gradient of the tangent to \(y=f(x)\) at \(x=8\). (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only \(\text{Gradient of tangent }=1\) Show Worked Solution \(f(x)\) \(=6 \sqrt{x+1}+5\) \(f^{\prime}(x)\) \(=6 \times \dfrac{1}{2} \times(x+1)^{-\tfrac{1}{2}}=\dfrac{3}{\sqrt{x+1}}\) \(\text{At} \ \ x=8:\) \(f^{\prime}(x)=\dfrac{3}{\sqrt{8+1}}=1\) \(\therefore \ \text{Gradient of tangent }=1\)