(1 point) Find the linearization $L(x)$ of the function $f(x)=x^{3 / 4}$ at $x=1$. Answer: $L(x)=$

Step 1 ：Find \(f(a)\) where \(a = 1\), so \(f(a) = f(1) = (1)^{3/4} = 1\).

Step 2 ：Find \(f'(a)\). The derivative of \(f(x) = x^{3/4}\) is \(f'(x) = \frac{3}{4}x^{-1/4}\). So, \(f'(1) = \frac{3}{4}(1)^{-1/4} = \frac{3}{4}\).

Step 3 ：Substitute \(a\), \(f(a)\), and \(f'(a)\) into the formula to get the linearization of the function: \(L(x) = 1 + \frac{3}{4}(x - 1)\).

Step 4 ：\(\boxed{L(x) = 1 + \frac{3}{4}(x - 1)}\) is the linearization of the function \(f(x) = x^{3/4}\) at \(x = 1\).