I can't factor f(x)=-2x^3+21x^2-36x+2 to find the critical values of f. HELP!

Question

accessdenied · Answer

What is a  'critical value''?  You mean, the points on f where the derivative is 0 or undefined...?

anonymous · Answer

yes. I have to find critical values and evaluate whether the intervals are increasing, dcreasing. I'm lousy at factoring. I don't see how this can factor.

accessdenied · Answer

We have to find the derivative first.  That'll give you a quadratic derivative, which is easier to factor.

anonymous · Answer

A critical number is an X value in the domain of f where either f(x) =0 or does not exist

anonymous · Answer

Sooo, I find the derivative of f(x) first?

anonymous · Answer

...hello?

accessdenied · Answer

ugh... yes
sorry, for whatever reason, i kept getting kicked off the site before my reply could even be sent.

accessdenied · Answer

if you found the x-values for f(x) = 0, you'd get the points where the graph goes over the x-axis, it won't really tell us anything else.

We find the derivative of f(x) and set that equal to zero -- the reason we do that is because, when the graph hits a maximum or minimum, which is a critical point, the graph hits a point where the slope is zero (there are other places for the derivative to be 0, and other places where there can be an extrema, but this is just a basic situation)

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