Question
I have tried to solve this problem over and over but my work doesnt even match up with the possible answers.... am i even solving the correct way?
QUESTION:In which interval is the function f(x) = x^3 + 6x^2 + 9x + 1 increasing??
A. (- infinity, -3) only
B. (-3, -1) only
C. (-1, infinity) only
D. (-infinity, -3) U (-1, infinity)
E.(- infinity, -3) U (1, infinity)
MY WORK: f '(x) = 3x^2 + 12x + 9 = 0
3x^2 + 12x = -9
3x(x + 4) = -9
x = -3 x = -13.... what am i doing wrong?
Answer
In order to find critical values, you're right that it helps to solve f'(x)=0. However, the solutions of 3x^2 + 12x = -9 are not found as you laid out. (To see why, note that in order for your method to work, you'd need to have 3x = -9 AND x+4 = 1, simultaneously (this never happens, since -3+1 = -1). Try going back and factoring 3x^2 +12x - 9 (which can only equal 0 if one of its factors equals 0). You might want to factor out the 3 first, since the only way 3x^2 + 12x +9 can be 0 is if x^2 + 4x +3 = 0. (since 3 times something will be 0 only if the "something" is 0). This should give you the critical values of f, which will lead you to the solution. http://vrd.askvrd.org/services/answerschema.xml
