# How do you find the critical numbers for #f(x) = 3x^4 + 4x^3 - 12x^2 + 5# to determine the maximum and minimum?

##### 1 Answer

Critical points occur at

#### Explanation:

Critical point occur where the derivative of the function is equal to zero.

Given

First derivative:

which can be factored as

Which implies the critical points (when

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While not explicitly asked for in this question,

you can determine if each of these critical points is a minimum or maximum by evaluating the second derivative at each critical value.

Results greater than zero indicate a local minimum;

results less than zero indicate a local maximum;

results equal to zero indicate an inflection point.

Here is the graph for verification: