SOLUTION: Find all of the critical points for f(x). f (x) = x^3 + 10x^2 + 25x - 50 One critical point is (-5/3, -1850/27). What is the remaining critical point?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find all of the critical points for f(x). f (x) = x^3 + 10x^2 + 25x - 50 One critical point is (-5/3, -1850/27). What is the remaining critical point?      Log On


   

Question 414181: Find all of the critical points for f(x).
f (x) = x^3 + 10x^2 + 25x - 50
One critical point is (-5/3, -1850/27).
What is the remaining critical point?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The derivative of f(x) is given by

%28d%2Fdx%29f%28x%29+=+3x%5E2+%2B+20x+%2B+25 (applying the power rule)

The critical points occur when %28d%2Fdx%29f%28x%29+=+0, i.e.

3x%5E2+%2B+20x+%2B+25+=+0

x+=+%28-20+%2B-+sqrt%28400+-+300%29%29%2F6+=+%28-20+%2B-+10%29%2F6 = -5/3 and -5. f(5) = -125 + 250 + (-125) - 50 = -50, so (-5, -50) is the other critical point (sorry I accidentally replaced -5 into f'(x) instead of f(x) so I just revised my answer).