Consider the function f x( )= +x3 2x2 –3 .
(a) graph the function.
(b) what are the x- and y-intercepts of the graph?

The graph is shown below.

x intercept is and y intercept is

Step-by-step explanation:

Given:

The function,

In order to plot the function, we need to find some points on the graph.

Let

Let

Let

Let

So, the points are

Now, as tends to negative infinity, also tends to negative infinity. Also for tending to positive infinity, tends to positive infinity.

Now, let us check points of maxima and minima.

For that, we find derivative of and equate it to 0.

.

For

For

As -1.815 > -3,

So, maximum occurs at and minimum occurs at .

Now, we plot the graph using all the above points and the maximum and minimum point.

The x intercept is when . From the graph, we get x intercept as .

Also, from the graph, y intercept is when is 0 and the point on the graph is  .

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step-by-step explanation: