SOLUTION: Determine, approximately using a graph, the intervals on which the function f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing.

Algebra ->  Rational-functions -> SOLUTION: Determine, approximately using a graph, the intervals on which the function f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing.       Log On


   

Question 87220: Determine, approximately using a graph, the intervals on which the function
f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 + 3x^2 - 7x - 1
A function will change from decreasing to increasing or vise versa after hitting a peak or a valley (a minima or maxima).
graph%28300%2C300%2C-5%2C5%2C-5%2C20%2Cx%5E3+%2B+3x%5E2+-+7x+-+1%29
Approx. at -3 and 1 the function changes signs.
Exact:
f(x) = x^3 + 3x^2 - 7x - 1
f'(x) = 3x^2 + 6x - 7
0 = 3x^2 + 6x - 7
7 = 3x^2 + 6x
7/3 = x^2 + 2x
10/3 = (x + 1)^2
-1 +- sqrt(10/3) = x
When: x < -1 - sqrt(10/3) .. the function is increasing
When: -1 - sqrt(10/3) < x < -1 + sqrt(10/3) .. the function is decreasing
When: -1 + sqrt(10/3) < x .. the function is increasing again