a) Use the chart to analyse each interval or specific x value (e.g., x = 0) to determine how the graph of the function could look. Describe what is happening to the function in each interval or specific x value by using the slopes of the tangents.
b) Try to sketch a graph of y = h(x).
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`h'(x)<0` when `x<0`
`h'(x)=0 when x=0`
Integrate h'(x) with respect to x
`f(x)=x^3/3-x^2+c` .c is an arbitrary constant, let c=0
Function is defined for all real number.The graph of f(x) (in red) and tangent to graph at x=-1 (black line).Tangent to graph at x=o it is x-axis .
The graph of f(x) (in red) and tangent to graph at x=1 (black line).Tangent to graph at x=2 and x=3 respectively in blue and green lines.
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