Derivatives from a graph Let F = f + g and G = 3f - g, where the graphs of f and g are shown in the figure. Find the following derivatives.
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G'(2)

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the derivative of the function G at x = 2, where G is defined as G = 3f - g.
2. Step 2: Use the linearity of derivatives. The derivative of G, G'(x), can be found using the rule: G'(x) = (3f - g)' = 3f'(x) - g'(x).
3. Step 3: Evaluate the derivatives of f and g at x = 2. From the graph, determine the slopes of the tangent lines to the curves of f and g at x = 2, which represent f'(2) and g'(2) respectively.
4. Step 4: Substitute the values of f'(2) and g'(2) into the expression for G'(2). This gives G'(2) = 3f'(2) - g'(2).
5. Step 5: Calculate G'(2) using the values obtained from the graph. This will give you the rate of change of G at x = 2.