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(Solved): The graph of \( f(x) \) has the following properties. i) \( f(x) \) is increasing when \( x1 \); i ...
The graph of \( f(x) \) has the following properties. i) \( f(x) \) is increasing when \( x<-1 \) or \( x>1 \); ii) \( f(x) \) is decreasing on the interval \( -10 \). Sketch a possible graph of \( f^{\prime}(x) \). Explain why there is more than one possible graph for \( f^{\prime}(x) \).
The graph of the derivative function \( f^{\prime}(x) \) of a function \( f(x) \) is shown in the diagram. Complete the chart using the graph of \( f^{\prime}(x) \). i) the intervals where \( f(x) \) is increasing ii) the intervals where \( f(x) \) is decreasing iii) the \( x \)-coordinate for all local extrema of \( f(x) \) iv) the \( x \)-coordinate for the point of inflection of \( f(x) \) v) Sketch the graph of \( f(x) \) if \( f(0)=1 \)
The graphs of the first derivative \( f^{\prime}(x) \) and the second derivative \( f^{\prime \prime}(x) \) of a function \( f(x) \) are shown below. Using the graphs, determine the \( x \)-coordinate for all the local extrema of \( f(x) \). Justify your answer.