Questions: Find f'(−2) when f(x)=x^2.

Transcript text: Find $f^{\prime}(-2)$ when $f(x)=x^{2}$.

Solution

Step 1: Find the derivative of $ f(x) $

Given the function $ f(x) = x^{2} $, we first find its derivative. The derivative of $ x^{2} $ with respect to $ x $ is: \[ f^{\prime}(x) = 2x \]

Step 2: Evaluate the derivative at $ x = -2 $

To find $ f^{\prime}(-2) $, substitute $ x = -2 $ into the derivative: \[ f^{\prime}(-2) = 2(-2) = -4 \]

\[ \boxed{f^{\prime}(-2) = -4} \]

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