Word Count : 358

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We are given a function: $$ f(x) = 2x^2 + e^{3x} $$ We want to approximate the derivative at $x = 2$ using: $$ \frac{df(x)}{dx} \approx \frac{f(x+h) - f(x)}{h} $$ And compute for: * (i) $h = 0.5$ * (ii) $h = 0.05$ Then determine: * True error = $f'(x)_{\text{true}} - f'(x)_{\text{approx}}$ * Relative true error = $\frac{\text{True error}}{f'(x)_{\text{true}}} \times 100\%$ --- ### Step 1: Find the true derivative $f'(x)$ Given: _________ _________ _________ _______ ____ _________ _________ __________ ________ _______.
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