A) Graph the function and label all zeros. Be sure to label the axis and what you are incrementing by. b) List the following. Answers may be approximate.
Absolute Max
Absolute Min:
Local Max:
Local Min

9514 1404 393

Step-by-step explanation:

The function is odd degree so has no absolute maximum or minimum. It factors as ...

  g(x) = x^2(x -5)

so has zeros at x=0 (multiplicity 2, meaning this is a local maximum*) and x=5.

Differentiating, we find the derivative of g(x) is zero at x = 0 and x = 10/3.

  g'(x) = 3x^2 -10x = x(3x -10)   ⇒   x=0 and x=10/3 are critical points

The value of g(10/3) is a local minimum. That value is ...

  g(10/3) = (10/3)^2((10-15)/3) = -500/27 ≈ -18.519

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The local maximum is (0, 0); the local minimum is (10/3, -500/27). The graph is shown below.

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* When a root has even multiplicity, the graph does not cross the x-axis. That means the root corresponds to a local extremum. Since this is the left-most root of an odd-degree function with a positive leading coefficient, it is a local maximum. (The function is increasing left of the left-most turning point.)

step-by-step explanation:

0,0

step-by-step explanation: