Let f (x) = 12x^2 ? 3x^4. Use the First or Second Derivative Test to find the re

Question

Let f (x) = 12x^2 ? 3x^4. Use the First or Second Derivative Test to find the relative extreme values for f. Then identify the behavior of the tails of the function. Sketch the graph of the function following directions above and turn it in during your discussion section on the day this assignment is due. In the answer blanks below, fill in the appropriate x-values and corresponding relative extreme values, with the x-values in increasing order. Relative Maximum Values: f( )=() f( )=() Relative Minimum Values: f( )=() f( )=() Choose the letter of the graph that best shows the tail behavior of f

Explanation / Answer

1. The thing to do is find the first and second derivitive of f(x).

2. After you find the first derivative, set it equal to zero to find your critical points.

(Additional crictical points are determined when the first deriviate is undefined.)

3. Substitute the critical points from step 2 into the Second Derivative. If f''>0 then the critical point is a relative minimum; If f''<0 then the critical point is a relative maximum. If f''=0 then, you will need to use the first derivative test to find the extrema.

As for end behavior, the negative quartic acts like a negative quadratic function.

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