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)*.

### 1 Answer | Add Yours

Let

`h'(x)=x(x-2)`

`h'(x)<0` when `x<0`

`h'(x)=0 when x=0`

`h'(x)=0when 0<x<2`

`h'(x)=0when x=2`

`h'(x)>0when x>2`

Integrate h'(x) with respect to x

`f(x)=x^3/3-x^2+c` .c is an arbitrary constant, let c=0

`f(x)=x^3/3-x^2`

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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