14 Given $f (x) = x (1 - 3 x^{2}), f^{'} (- 1)$ equals:
$\begin{array}{ll} A & - 8 \\ B & - 5 \\ C & 2 \\ D & 6 \\ E & 10 \end{array}$

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Answer

$f^{'} (- 1) = - 8$

Steps

Step 1 ：Given the function $f (x) = x (1 - 3 x^{2})$ , we want to find $f^{'} (- 1)$ .

Step 2 ：First, we need to find the derivatives of $u (x) = x$ and $v (x) = 1 - 3 x^{2}$ .

Step 3 ： $u^{'} (x) = 1$ and $v^{'} (x) = - 6 x$ .

Step 4 ：Using the product rule, $f^{'} (x) = u^{'} (x) v (x) + u (x) v^{'} (x) = 1 (1 - 3 x^{2}) + x (- 6 x) = 1 - 9 x^{2}$ .

Step 5 ：Finally, we evaluate the derivative at $x = - 1$ : $f^{'} (- 1) = 1 - 9 (- 1)^{2} = 1 - 9 = - 8$ .

Step 6 ： $f^{'} (- 1) = - 8$