# SOLUTION: Over which intervals are decreasing? f(x) = x^3 – 12 x^2 + 36x + 1 I came up with (-6, -2), is this correct? Also, I am trying to find the locations of the relative extrema

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Over which intervals are decreasing? f(x) = x^3 – 12 x^2 + 36x + 1 I came up with (-6, -2), is this correct? Also, I am trying to find the locations of the relative extrema       Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Rational Functions, analyzing and graphing Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Rational-functions Question 127038: Over which intervals are decreasing? f(x) = x^3 – 12 x^2 + 36x + 1 I came up with (-6, -2), is this correct? Also, I am trying to find the locations of the relative extrema for: y = (x^2 + 5x + 3)/(x – 1) I have been working on this one for some time and came up with (4, 1), (-2, 13). Does this look correct? Thank you so much for your guidance. Answer by stanbon(57940)   (Show Source): You can put this solution on YOUR website!Over which intervals are decreasing? f(x) = x^3 – 12 x^2 + 36x + 1 f'(x) = 3x^2 - 24x + 36 ------------------ f is decreasing when f'(x) is negative: 3x^2-24x+36 < 0 x^2-8x+12 < 0 (x-6)(x-2)<0 Plot the points x=2 and x=6 on a number line. Find which intervals contain the solutions: x=0 does not work x=4 gives (-2)(2)<0 which is true x=10 does not work So your answer is correct: I came up with (-6, -2), is this correct? ===================================================== Also, I am trying to find the locations of the relative extrema for: y = (x^2 + 5x + 3)/(x – 1) f'(x) = [(x-1)*(2x+5)-(x^2+5x+3)]/(x-1)^2 f'(x) = [2x^2+3x-5-x^2-5x-3]/(x-1)^2 Relative extrema exist where f'(x) = 0 [x^2-2x-8]=0 (x-4)(x+2)=0 x = -2 and x=4 You have relative extrema at x=-2 and at x=4 Your answers are correct. ---------------------------------- I have been working on this one for some time and came up with (4, 1), (-2, 13). Does this look correct? Thank you so much for your guidance. ========================= Cheers, Stan H.