# Calculus Problem on Derivatives## Instructions**7. READ CAREFULLY.** The graphs of \( f \) and \( g \) are shown below.### (a) Evaluate \(\frac{d}{dx}[f(x)g(2x)]\) when \( x = 1 \), if possible. If it is not possible or the derivative does not exist, explain how you know.### (b)Evaluate \( F'(0) \) where \( F(x) = f(g(x)) \), if possible. If not possible or the derivative does not exist, explain why.## Graphs### Graph 1: \( y = f(x) \)- The graph of \( f(x) \) is composed of line segments.- It starts from \((-3, 2)\), remains constant till \((0, 2)\).- There is a sharp corner at the origin.- Then it decreases linearly to a minimum point at \((2, -2)\).- Finally, it increases linearly beyond \((3, 2)\).### Graph 2: \( y = g(x) \)- The graph of \( g(x) \) consists of two distinct linear segments.- It begins at \((-2, 0)\) and increases linearly to \((1, 2)\).- A break occurs, segmented to another linear decrease from \((2, 2)\) to \((3, -1)\).

Name: # Calculus Problem on Derivatives## Instructions**7. READ CAREFULLY.*
Uploaded: 2024-03-20T06:46:42.000Z
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Description: # Calculus Problem on Derivatives## Instructions**7. READ CAREFULLY.** The graphs of \( f \) and \( g \) are shown below.### (a) Evaluate \(\frac{d}{dx}[f(x)g(2x)]\) when \( x = 1 \), if possible. If it is not possible or the derivative does not ex