Asked by Emma
                Determine the y-coordinate of the local minimum on the graph of the function f(x) = x5 - 6x2 + x + 4.
            
            
        Answers
                    Answered by
            Reiny
            
    f(x) = x^5 - 6x^2 + x + 4
f '(x) = 5x^4 - 12x + 1
= 0 for a max/min
Not an easy equation to solve,
Wolfram shows two real solutions,
x = appr 1.3098 or x = appr .08335
http://www.wolframalpha.com/input/?i=5x%5E4+-+12x+%2B+1+%3D+0
f(1.3098) = -1.129
f(.08335) = 4.04167
so the y of the local min is appr -1.129
    
f '(x) = 5x^4 - 12x + 1
= 0 for a max/min
Not an easy equation to solve,
Wolfram shows two real solutions,
x = appr 1.3098 or x = appr .08335
http://www.wolframalpha.com/input/?i=5x%5E4+-+12x+%2B+1+%3D+0
f(1.3098) = -1.129
f(.08335) = 4.04167
so the y of the local min is appr -1.129
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.