Question
Determine the y-coordinate of the local minimum on the graph of the function f(x) = x5 - 6x2 + x + 4.
Answers
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