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Determine the second derivative of \( f \) and call it \( h \). Then sketch the graph of \( h \) on the same system of axes as \( f \) and \( g \) in ANNEXURE A. Clearly indicate all intercepts with the axes.

Ask by Johnston Chambers. in South Africa
Mar 13,2025

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To find the second derivative \( h \) of function \( f \), first find \( f' \) by differentiating \( f \), then find \( h = f'' \) by differentiating \( f' \). After that, sketch \( h \) on the same graph as \( f \) and \( g \) from ANNEXURE A, marking all intercepts with the axes. Please provide the specific function \( f \) for detailed calculations.

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The Deep Dive

To determine the second derivative of a function \( f \), you will first need to find its first derivative \( f' \) and then differentiate that again to get the second derivative \( h = f'' \). Once you have \( h \), sketching the graph involves plotting the values of \( h \) against \( x \), while also showing the original function \( f \) and another function \( g \) if provided in ANNEXURE A. Look for key points such as intercepts with the axes where \( h(x) = 0 \) or where it crosses the y-axis. For the intercepts, you’ll mark the points where the graph touches the axes: the x-intercepts are found by setting \( h(x) = 0 \), and the y-intercept can be determined by evaluating \( h(0) \) (if defined). Don’t forget to label your axes and curves to clearly differentiate between \( f \), \( g \), and \( h \). Happy sketching!

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