Friday
April 18, 2014

Homework Help: Calculus

Posted by Nikki on Monday, May 10, 2010 at 7:57pm.

How many critical points does the function

f(x) = [(x-2)^5][(x+3)^4] have?

A. 1
B. 2
C. 3
D. 5
E. 9

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Ok, these are my thoughts on this question:
My impulse was to do derivative of the function. However, if I'm going to set the function equal to zero to find some critical points (because a critical point is where derivative either equals zero or doesn't exist), it's going to take me forever, and this question shouldn't take very long.

So my next choice was to look at the function itself. The degrees are 5 and 4, so if we add those degrees together we get 9. Essentially, I thought the answer would be E because of 9 factors, 9 CPs. However, the factors repeat, 2 and -3!

Thus, my guess is B, which is two. Are my reasonings right?

Thanks much!

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